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Topics in String Theory | Lecture 4

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let's go back to roared to try their of before Tripoli but there is always some of whose except came 3rd keep making it up fast after Umberto here bravura younger could so we're introduced rings do we done before let's go back so what we learned about geometry or a black hole near horizon near the horizon we found out that it was just pretty much good old flat space-time approximately very very close verizon and we describe it by a particular matter at 1st but this week we started of course with the ghost watch over Arctic always made a bunch of changes of variables In particular instead of beef Schwartz shelled corn are never enough here the Swat chilled quarter aura goes into the Schwartz the usual way we'd replaced it Oakland we replaced by another variable which was actually the proper distance from the horizon aura is not a proper distance from horizon overall that's its definition of a definition of raw proper distance from the horizon and I won't bother writing down the relationship between now and not terribly important all but role at 1 thing is important when aimed at a point when armed is equal to what mn Judy busses short show radius of support for horizon at that Point role is equal to 0 proper distance from the horizon we also made another change of variables on May God which
is a kind of variable was equally Anderson dimension was variable is equal to what time divided by 4 M G so roughly speaking all in every place here she is equal to 1 or 2 years ago roughly where Omega Tomlin Lane a measure missing units with use Cooper award tool GE is the Schwartz till the radius of so a path from a factor of 2 major measured in units of the short radius and also make it affords dimensionless worse because of the ratio of time by Barbara Schwartz a reduced and we did that went a little exercise was a number of steps more steps God but never rests with their it we found out that year the horizon of the black hole we called near horizon geometry drive proper distance was equal from minors Rose squared the Omega squared hiker right doesn't have the proper time difference between proper distance square proper Times Square is just change starting to Ukiah my deep square group plus sign here mega squared plus and then there was another Peace coming from angles on horizon but I'm not terribly interested I'm interested in distance from the horizon and time two-dimensional picture of a black or just time and distance from the black or this is what the automatic is like not point that to you that this method is very very similar the metric of ordinary flat space conventional flat space the surface of this round table here in polar according to the poll course we will ordinarily right and arrived here because I don't confuse it with their spot ordinarily and Pollock coronach played a role Dr school a musical from square d data squared plus Bureau square so I look very similar to each other no difference it minus sign that Omega is analogous it's a hyperbolic angle just a finished yard starts corrupt acts as a slap space ordinary space this happens to be nothing but ordinary flat space time I kind of Paul caught me there are a reference for everybody remember this and Omega Is he or foreign duty now this is the metric close to black authorized would draw a picture of us this is just flat space import coordinates looks somebody like areas Omega of hyperbolic angle variable which way down the remote past Omega is equal to minus infinity way up here Omega Siegel plus Infiniti M Raul lines of
constant rolled just had problems which require further and use the high-rise right over here there's a horizons for ride over Vera if we call along a line of constant or make a fixed time that point right over there it is Our 20 it's role equals but it's are equals to and so utterly set up last time we also said that the horizon of the black hole well the general arrives rice this 2 notions of Verizon and to each 1 is called by 4 could arise for you were the bifurcate horizon it is simply this point over here and the bio North Fork it means buying who would Emmett Till nest on the intersection of these 2 white he bifurcate horizon was another notion of Ferrari and doughnut motion of horizons is more physically interesting 1 just Hall like like surfaced here why is an interesting well if somebody gets stuck behind that quite like surfers we cannot send a message to the outside we cannot send a message out beyond that like surfers salt this is a kind of horizons I want you behind it you can get any information distances beyond year Oracle's to an overall recalled Oracle swam all row greater than 0 OK that's the geometry of the near horizon were not only go very very far from the black hole we go very far from the black hole we see also id looks like spaced our books for flat cars but he is a metric that we would see we take the Schwartz film that growth for chill that were struck down the U.S. squares is you got 1 minus 2 NGO are D key squares last won all although 1 to G or what are squared and now we go far from the black or which means are Oral very large what happened this word oryzivora launched this is Dedie Square may just be cons he squared plus or minus D D squared plus br square but corporate all are enrolled fast from the black hole foreign role on once way far away from the black hole the proper distance of the black or was approximately just aura the only near the black Matt all In are very different from each other but when your father from the black hole raises is just radius distance from the horizon is basically the same as it would be a flat space so far from the black hole Roman are basically the same thing this factor here is not interesting first one respect that he also was born we just get my he squared past br square but so far from the black hole and Diaz squared areas Martinez rose squared but what's right sorry British square use me and deep he squared euphoric he squared because there is no interest in fact so as deeply squared piece squared theaters 16 M squared G Square D Omega squared what I've done here is just multiplied by 4 MG so that all may get she is a group of foreign GE terms Omega at this peace here and then the other pieces just squared euro square justice or here making use of the fact that role all of the same thing for from work or who were traveling bag near the black hole the only difference only interesting difference between these 2 0 is not square terms but it's in the kind terms on make it is that kind of time is related time of this equation over here and on the 1 he and near the black or was a factor rose square when role always very very small me that kind runs very very slowly very for India the horizon of the black hole there was very little proper time in any appreciable bureau go for far from a black or this is Reforma or so OK this is curious what's going on how we think about this what kind of geometry of us all hard to envision that it's quite hard envisioned as you move away from the horizon of the black hole this they promised this mainly give set outright give you the best picture I can of what this geometry was like yacht my let's come over here this picture over here it's much easier to ah understand space this police part so let's come back to this picture and now imagine a geometry which has the following properties merely origin in looks like Rose squared status square postural square but far from the origin and looks like instead of raw square let's just say 16 Square G. squared off are deflator squared plus Bureau squares very similar to what's going on over here except when I'm dealing with space time we're dealing with just ordinary space what kind of geometry users a what looks like the U.S. you guess what looks like I'll show you may the origin and it looks like a what years when they draw this plane on age for years planned drawn edge on as I go around data Neely origin it looks like the plane pronounced removal away from the origin and what happens look at it instead of having this role squared here we just get a constant square the meaning of the fact is the distance around theta between 2 neighbouring values of data instead of depending on role just becomes comes from 16 M Square G. squares of share what looks like it looks like a cigar box cited geometry that looks like where the distance around a cigar this end here it is well faded goes from 0 to party so distance around the whole cigar and the start of a cigar band is more M. G times piety
pharaohs 0 2 fires you around Narrandera our arrest that sort of this end on the other hand very in theology and over here they really just does look like polar coordinates figures around coordinates very close to the tip of the cigar artwork flat any geometry in the vicinity of a point looks pretty flat but as you go out and as you move around this point here close to the tip of a cigar this is the matrix far from the tip of a cigar With this distance around the data does not depend on how far away you are a media in Omega when your far away he doesn't depend on rock when clause in the distance for a given Omega those world main message here Is this the current space it's a curved faced with curvature near the horizon and how does that curvature depend on a mingy well distance around this she said it is very very big when energy get big storm when the Mets lost when the Mets begets gets big distance around Syria's big and that means curvature of the tip of lest the Bigelow masses Norwest curvature of you have to proposed drug or West curved it is a small Maris who applied this highly curve this this is also truly the shortage of black called highly curved when the masses small new black or get near behind horizon missed with this point as the horizon it becomes a maps so becomes as point over here so you can get some feel for what this geometries like we are looking at it ordinary space version but still I think that's not completely satisfying River is worth reviews it is what it is the geometry the coefficient of the Omega square varies From and the horizon where squared for far from the horizons were just becomes a number the number being 16 M Square due square at best really all you really need to know about the or was this this strategy but we will get given angular separation factor in front of the Omega square tells us How much proper time areas from 1 Omega scoreless all made equals 0 let's call so maybe equals water yes I very close horizon where role was very small proper time distance between homemade equals 0 equals 1 is very small so near the horizon as kind flows as major flaw was very very little proper time between neighboring values of time to fly from the black hole neighboring values Paris aura kind of kind differences which are just number here which is nothing but DG Square OK so clerks sustain about Clark's clocks far away from the black or behave exactly as you would expect every read this time he clocks very close to the black hole we wrote times on maker wrote injuries from makers of prime variable scales differently close to a bicycle that's that's what call was like them off again outside the black called corresponds to Rome greater than 0 row grader 0 is all of these curves wrote 1 through wrote 3-year-old for at outside the black hole anybody stationed at rest outside the bar called if you could if you arrest outside a black hole Agarwal Ilse slowly for all of the black hole far away and you very very far away to pick along it doesn't take much effort to stay out of Iraq or you can orbit around the black Hole Merridew conditional Jet Propulsion device that can keep you out of a black hole and wraps moving along 1 of these trajectories he staying a certain distance away from a bar called on the other hand wants somebody passes through war will now call this the horizon the event horizon This is a bifurcated horizon misses the event horizon want you pass has the event horizon you cannot send a message to the outside world that's a character a black or so makes it a bark or a fair is that they feel like they caught feel like radio spew radio white waves always move on 45 in a drawing I ever draw on a cycle you otherwise because you otherwise bar the speed of light as a 45 degree or right so I'll following news that way all life trying to get out that way but get out stop why rays conforming but can far I 1 other singularity let's go back missed what your rhetoric which I've erased or bath for Rice arrived and see if we can trace will 1st first-order you back this part of our saying all but 3 shot what but the man a letter Tuesday as he arrived for few across the whole of our we can't say we can answer right now is Bob Bob riding on his trajectory is riding on his world wine more now will but was quite far from the black hole here are or maybe equals 0 0 maybe equals 1 0 maybe equals tool whereabouts which watch over time the usual time that Bob measures on wristwatch he measures Short your private well piano maker are basically the same thing except for a factor of foreign G so this would be his time equals 0 this would be his time equals foreign gene this would be his time equals 8 energy for so right
along here Bob is looking at his wristwatch and Cari Mr. King off reserve it is further number of checks along its trajectory he never falls into the black hole why not because I tell you he doesn't fall into the black hole he stays outside his or so we stays at a fixed proper distance means are fixed hyperboloid via a looks back but straw hours not Alice doesn't have to be our stars could be a proton it could be a fault it could be anything falling off moving in this direction let's say a photon
U.S. me about a four-part here's a photon fast fraud trial moves 45 degrees and it sure looks to me like it passes the horizon where are Bob Bob say so Bob's wristwatch off prime time in Sydney is way a way out there so he looks back from wherever it so you're Koran 1st problem shoe bomb looks back and sees the photo Owyhee YYC back look back any sees light coming to him from my from what white doesn't usually comes from our 5 strictly speaking Bob use for armor for bombs going away so it's not make a photon of maker Alice playing ouster houses following throw away at hand those year she falls through a mob looks at work so he is hurry here's how wave as Macon closer together which is waiting pretty rapid Ory along home world line Israeli Prime off I looking back from this point he sees our story here we all see each other slightly in the past 6 are white time get us so Bob house over here next after another in what time he sees Alice over here she waved a certain number of times Bob Alice way few what arms Bob looking back keeps looking back and Accorsi he and each 1 of these measurements each 1 of his observations is separated let's say by 1 2nd each 1 separated by 1 2nd along with trajectory here out he sees it fewer and fewer of Alice's waves unit time eventually is way out there a huge amount of part of his time and buyers but I don't see is 1 way of and then as he goes further and further into the distance future along has accelerated trajectory he sees Alaska way right over here but he never sees hours cross eyes cannot see Alice Krauss arrives salt from his point of view us waves slower and slower and slower and eventually just can't frozen Hall where she appears to be frozen on just just outside the horizon how close the horizon well the that point over here that corresponds some hyperbola not hyperboloid shows how far she used from horizon about Porter store that out the firm Bob respected please but a very easy time foes that dead there's the information does not say if this is classical picture of black hole do not account for a quarter character of Amir completely look what I will Bob actually imagine how you see her waving innings Lawrence she sending out right away a the light waves of Bob has sent out why where she said is allied with great taking electric charges in wiggling right it's at Adams who we're going of course Bob seas however as we go of terror charges where that save up White that Bob sees 1st at topical waves their becomes infrared eventually becomes long wavelength radio waves Barbizon Sialis anymore maybe his along with the radio compact fuel for waves but then our gets sold on frequency gets will also allow that not just of the sea anything so really strictly speaking Alice just days away she just days away from our Bob point of view a radiation most from being optical radiation from being thousands of miles long ago and Myron forever radio waves and longer sure Austria jury I'll ask what the CEC you might think maybe that means at our seas Bob speed up so it's local water out of their ass out the way of for a walk off the job I for life assure ban from your point of view I don't get squash this way guess twice this way if a formal Lawrence contraction just as what it sees Tullalah was our also backwards from in draw cleaner Alicea green but this is Alice's Clark houses Clark From the fingers special she looks back and see Bob disadvantages to want to see even after she passes the horizon she sees what she sees it is Bob accelerated away from her father
doesn't disappear from our are from our perspective when she crosses the horizon moral what does happen is she sees tonight accelerating away from Soweto happens over Our view of was juicy Bob speed up Bob hard slowdown down but she doesn't see Bob do anything special when she passed her eyes and Bob perfectly normal she consent to sit on our side he consent Harrer signals leaders and horror signals from young but she can he consent signals freckles this way he's sending personal but she cannot send him signals sought to calm one-way barrier arises a one-way that is a reality means a steamer as a matter of fact since he's accelerating away from her realizes registered his wife he's more more about 4 shifted from Red it our number and his life she sees him arrest he sees horror race if the until she alone was just days away it was completely a asymmetric that right about a batch of the picture Allison Bob for you the black hole a chief of houses others boss the pressure all Is that not just particles like protons for the year much harder to see but much harder to detect still chapter we readers or part of the book but it was a matter what about what Alice for black the last chapter of the book that part of the reason why not it moving it regretted tells its gate they just like the dark Lavelett da gravity to better half an you don't do not serve a really did wrapped up I thought that was full force the chief this feel like area guess ritual that America ought to be right virtual grab times have no trouble exceeding the speed of light watched true it is I'm standing here a long time look and feel my gravitational field whether such a feeling is a gravitational field that was created some time in the past wrote to you now I'm will suddenly the constraints on the speed of light Gravitt times tell you that you cannot see me moved all you won't feel me mingled your gravitational field I exert argue will not change until light gets a chance to get you what that they say white grabbed grabbed those at the same at speed if really I just also rule of electromagnetic fields if I were a highly charged and your arm were also highly charged we might be the repo whichever attracted Chavez disposal that With than that there would be a sewer steady-state situation are suddenly moved your wood only detect my field changing by who would be I don't know that this CD work rabbit doesn't just described its do not related fathers are way where tour where are you could just think garb as we are you look of gravitational field will make up the static gravitational field of a stationary object but they don't have to escape from the black or where they are you're them at the store rappers puzzle what you see when you watch your feet for food the Black course your falling perimeter was confused about that what happens when I see Dorsey my feet passed through a black hole horizon organizing Murphy patch of black or a or work set up that problem however is formally into a black hole here's feet wet Huffy fall through 1st changes following these 1st our feet on that drive draw feet just well here sir feet act can trust OK here's a that's a world line of her left for it the world line of her head was over here follows falls and waiter so Alice's feet years Our says head house is looking at her feet salt at this point our yet she certainly sees nothing but she sees a feet over here
Tuesday feet at the instant when she looks at them she sees a slightly in the past 2 hours to defeat from he at hours of what Alice sees feet From here are Alicea free from yes season from here but yacht tried she looks back and see white comedy 2 are from our feet he a light coming to us from our feet along a 45 45 degree angles on her particularly accurate but are supposed to be so icons from here How sees willing proposal follows a electrically charged sending white light he and his wife he and his wife is not point which the I wish you bursary her figure of course she doesn't see her feet from this point at the same Pine who promised point over here she does had actually managed the time she she's a feed from short we have chosen nothing special happens when she parishes of supposed Moorhead stays out of hole her feet which have already passed fully brought for the pastoral or achieve sizable rest remit nor I don't want to go where they were happen bats as bad as my birth for Stewart happened hours which head now so proud takes off and separated from our
feet there's no way that you can avoid he be torn off for our bodies by the acceleration of the keypad battle black also has to accelerate away from our feet now have feed might get called OK feel might get cold but they can't get hold fast enough to to keep up with it looks like keeping up with her but enough reason for hours as bomb goes faster and faster in the barbers accelerating away from the black hole can really accelerating standing still going standstill in a gravitational field with the same is accelerating so Bob accelerating away think about this now think Bob accelerating away end the distance to hours or our Baba mouse is now Robin Alice is dragging behind bomb at a fixed distance in your reference what is it like in barbed reference frame if the distance that hours In your reference frame arrest is fixed and bomb was going faster and faster what does bobsleigh about whilst oscillatory going opposite ways she's just getting Marcy's getting separated farther and farther be cost of Iran's contraction so bombs says Oh my goodness Alice is getting farther and farther away from even know observers arrest say that the house is a fixed distance away she get closer because she can't get past this white Kong she can't get up speed you can't grow fast rooms light eventually from Bob's point of view here just drag further and further and further behind happens not be Allison Barber happens to be our forces head and houses argues stretch that stretch away from harm a lot of bad things have way break so wants houses Cedar behind the horizon she has 2 alternatives fall in with them is no problem nothing unusual or stay out of the black or the issue will be over b feeding not solution of right ahead of you will go well so far we haven't discussed anything about the singularity of a black or white so let's not talk about the singularity of a black hole where is it on this charge here with his arms diagram of clean the Byron of ahead before but come back to the shore chill or 3 rightist what your address GTE squared times one-liners to energy of are With a minor signed plus sign 1 1 minus 2 MG all are br squares and those plans are for offering new accord suppressed at nite would be tour which has a negative sign is always kind you always recognized trying work time like variables by a minus sign from you recognize the space flight variables ordinary space by a positive sign but something happens when Orrin crosses to injury when I was greater than 2 20 this is possible and your Boris more 1 minus a small number of positive born August smaller Ventura G suddenly the deciding changes he assigned also changes here it means but somehow part is becoming kind like variable and cheese is becoming a space for verbal bestows not mean anything for Mac means spaced plans the time behind the black or this is a feature our peculiar set of coordinates when you has summarized and the coordinates interchange what's happening here is something like this if you were to move in all along that surface of constant time or the horizon you reject you would offer would be decreasing ah decreasing decreasing decreasing on Chile gets a toe injury and then I will go from then suddenly when past the horizon it becomes a kind like quarters are goes up that way for me what about f or maybe it is a little bigger or to use a little bigger Solway comment also horizons this is only 0 this is omega equals 1 1 unit of pine waiter also commented how we get this point here and then these coordinates each what chilled Corona's which a peculiar court suddenly make another header off so that funny court is nothing special happening over here it's just a choice of coordinates used where are on 1 side of the horizon are busy time like a space like variable on the other side of the horizon to plan herbal and vise versa and display space the time but nothing really is happening at this point just ordinary generic poring over spree started OK now let's go toe with the singularity you are the singularity is Oracle's 0 that's st place something very dramatic happening Mayor tidal forces become infinite curvature becomes infinite all hell breaks loose of a city or Irene as Oracle 0 start coming in we got Our equals To win G S R 0 then we continue all longer we are accessed because we are axis the PRI axis makes a right angle turned on chill we get tho are equal 0 and that's over here Our equals 0 we do the same thing will occur the Oracle 0 over here if we can make all the points correspond Oracle 0 together it looks like it looks like a hyperbola for a book that hyperbola is a
singularity strike having a nasty wicked points because it's highly curved and very unpleasant use also originally met singularity was placed a place means other places a vertical world warned but not placed at a time of war along here the singularity occurs after a certain amount of time not really a place kind of Collins says a singularity the place OK let's let's think about now 4 hours who wear headers falling behind the horizon he she's over here where she go next to want to escape the terrible fate of far falling into a singularity she did try to get out watching and try to go that way eel way she cannot escape was always chicken with here without exceeding the speed of light she cannot escape the fate of formed from a singularity so that's another property once you pass the horizon at you have no chance but before posting Ali kick you communicate with the outside for you doing doomed by the singularity and that there was 1 more feature on a black hole mathematics on this matter now we Contel real curiosity but a mathematical artifact which we're going to find doesn't really mean anything physical but still was a mathematical artifact this geometry here is the same refuter Inc Hi missed pouring fact these coefficients don't depend on time altogether and what happens to be he square if we take time from Wang part set ashamed this electric here is what a physicist would call kind reversal and invariant and looks the same going forward His going backward are still the peculiar because you could see over here back forward and part was a singularity what implies is that there must be a singularity also in the past study this metric in mathematical detail you'll find out that would really represents the kind symmetric situation with the singularity in the past has a singularity in the future now Alice doesn't have to worry about the singularity in the past nor wasting it back the past you take it back to the past she a story about a singularity in the future she volatility of the in your area we're here but let's just say think of Alice's history from armored instead the meaning of saying that something is crying reversal invariant is the same as saying that a particular history if you want to run it backward your watching watching the events taking place and you with run them backward meeting to say he would take a film of them and run the film backward back-to-back would fill were also be all possible history which makes as a solution of the equations of fury that's what it means for something to to be car reversible equations of general relativity are completely time reversible so anything can happen forward could also happen backward so let's think about what that means it is a history Johnson the Blackoak and weighs up on the singularity as she passes the horizon Bob loses track of can't see her well if that's a possible history we should be able of folder over save another possible solution of the equations which Alice was created at the singularity and jumps however the black hole 411 Bob looking back in the black all of cheers and no trouble going this way knowledge on oral she kid across our wood from here while the Yavapai reversal that has nothing to do with the ability to to get out of this this is called a pasteurized cars has no trouble or getting out of a pasteurized it's simply that kind reversal of the statement that Alice had no trouble falling into the horizon B time leverage Our passing I would use arises from research passing in is passing so she can pass it does not arise in the future she compares pass out the pasteurized and was Bob see Bob looks back and see something silly he sees a out ejected out of his black hole that's silly of course tried Camino nonsense and so something wrong with this picture will find that were no not anon this is Bob over here but actually seems to be able to see the singularity that's still a little bit annoying you look back and sees the singularity and then he suddenly seized allies jumped out from the singularity quotas Ekwall ignore call was nonsensical our configuration fiction it yes it that well the 1st thing is yes it is possible that likely know it's unlikely physical Whitehall a white or Whitehall now holes on existing owners is also an issue reverses this farmers not hearing is going way ordinarily does this is not time this is this is fictional this is not something that makes our friends on it's about pairs likely was by newer more works a good example you evaporate water from Pavel and jury and a space instead UCR water a materialized from space on scan happy candidates called the conversation about their a bomb explodes a bomb explodes and her sons garbage or replaced that's a possible history of this saying
Newton's equations for a bunch of particles where her you start with a bomb 1 of these are old-fashioned bombs are Bolsheviks carried around refuse require my grandfather would have hinges and UN or while bones and stuff gets Scavotto overpriced you'd be pretty damn surprised to see a bunch of stuff flying inward reassembling the bomb and Doria very delicately so that eventually it just had a little bit of a flame at the end of it that doesn't happen right away merits a possible solution of the equations of fear of a new series notice theory is completely time reversible saw what's wrong Botha possible but we know very well that 1 of them is not possible OK what do the Justice is thrown were observed how young center 1 of them is clearly extremely unlikely the other Israel likely the book possible With is 1st process where stuff comes in and creates bomber all you have to do is move was Mike kiII kiII fractions or molecular systems in the incident state the completely on duly ability to work to create a bomb it's extremely unstable backward trajectory it's sort of like magic I have very high now the critical point it's very easy to roll a ball off the top starting at rest Durocher Hang Hazel kick where we call for the probability that I will fall that mountain is extremely hard to reverse trajectory is possible throwing the ball off to war and just getting off work extremely unlikely that tiniest little a wind-up missing the cop another example everybody here play pool when they were kids billiards your now course a cars you start with all the billiard balls or we urge those balls rack proper triangle perfect triangle from Reeva Mark 15 right then a cue ball he good Marge Schott scattering all over the place high probability that the scatter it would be rather amazing to see 15 billion balls even if we can worry about friction on on the table will be rather amazing to see 15 billion balls calm together and form a perfect triangle with a cue or lineup that way pretty young might right but also there are solutions of the same equation of both possible from the point of view the equation but the differences that his star those 15 16 balls In a configuration which was John they reassembled into a triangle and then previous little arrow you would miss the trial completely in all you would make would be a table full of billiard balls going random direction it also is just as unlikely that you would have precisely the same thing when the other way but retired yes EGF each of these are quite yet yes that was correct but you know if you were just to say I'm not I'm I'm watching this thing NYC is billiard ball scattered all over the place YouTube is over and over and over again you we get more or less the the same pattern every time billiard ball scattered all over the place and West you following believed both carefully you would notice that was a particular our differences but you would notice if the billiard balls came together form a triangle so yes you're right that means any given think to pointers giving configuration is very unlikely that or entropy comes in hour barred 1 baht seen here ultimately going to understand this in terms of the entropy of a black or white board Barber scene he what we now understand this he seen 1 of these varied very unlikely process on possible brushes but unlikely were a black hole just sitting there suddenly spots are where you have a full-fledged version of the house but not likely that Alice falls into the black hole so it really is very very much the same thing will find out that this is 1 of the aspects of black holes it has to do with their entropy good discovered black coal Senator Carl there and thermal equilibrium they have stumbled properties it was say the same thing about how hot water what the likelihood that if you drop an ice cube part of hot water that it will form a melted configuration with a worry reduced forgive more water in power more very hard right what's the the probability is wait 1 that pot heist you will get ejected out but also will satisfy the scene equations both of quantum mechanics of classical mechanics so In that sense for a possible the same thing going on here the horizon of the black hole has entropy just like a pot of water he information very rarely itinerary were the entropy of a black hole of media part of water a somewhat softened Cube same thing here very rarely widow over garbage on the horizon of the black coal assemble itself and rejecting a house it is really all about is that it could be below its combination of quantum mechanical from more from normal fluctuations Mayor Kwame mechanical fluctuations both where he worked on in the case of a hot water of course it's mostly thermal Greg OK let's take a five-minute break a former Penrose diagrams of talk about actually making black holes are you actually make a black hole and Wii half of this diagram namely the bottom half is completely on physical it's not something you ever really have to worry about the bottom half which is peculiar half of the Whitehall young Michael asked me a question and I realized her as questions that I was using a bit jargon clarify the judges are used I told you that role was
proper distance from the horizon jargon mayor was proper spends Lemay just remind you worked proper distance means a piece of
drug and it some similar the proper arm was proper time along 80 observers trajectory measure measures wristwatch time right was wristwatch time along on her right right now we have heater Bob I must say Bob Wright at time equal 0 draws Stratus Have you can still the horizon In this case a straight line was mean to say that this is a given proper distance away from the horizon we are now have said this is measured by real yardsticks are sticks the In this room we don't our yardsticks newsroom meters 6 distance measured were honest leader specks of tropical means after that To say now Will are wearers little are up there because erased OR over here does not measure proper distance just a mathematical quarter which is not proper districts thousand measure rheometer sticks distance rows things you need expects sold Codorus jargon but sometimes I forget OK hack now let's talk about our Penrose diagrams Penrose diagrams of great there really are are the weight stand all kinds of things and and very easy easy to think about easy to draw a little bit difficult to actually work hours detail but we don't need to work American detail let's space time a black eye for an eye and in particular let's draw just ordinary flat based on the blackboard William another dimensions on a blackboard to draw four-dimensional space so let's pick out tool coordinates 1 will be kind and the other will be distance from the origin ordinary flat space-time so it could be funeral Taiwan's vertically upward she said overall is just distance from the origin he ever saw Enron Soros where Aurore axis we can make a great out of this month chopping up climaxes doing the holes and extrapolating them horizontally we can make our vertical grid 1st point here is wrong recalls 0 incident with nothing to the left is by definition role was always possible proper distance from the use of polo coordinate their kind of Our corn always positive and here it his all space this is role equals 0 Longview Road goes 1 roller coaster Roller Coaster 3 keyhole 0 she was 1 of my warned Prime can get negative in this picture and this is the history of the whole universe on light waves let's say light wave that comes in from remote past columns and hits the origin what happens if it hits the origin it is go back out is not really bouncing off anything it's just physiology registers origin discover right through the origin but poll or comes union goes out Cerezo waiver from doing out a little light wave might come in later bounced out and so forth again that's the history of the world on a small board was not the history of the whole world is but backward isn't big enough to to describe the whole world the whole world meaning all infinite distances Apple infinity and all infinite times from my innocence in the past so what relatives due resume a quarter transformation from our theories or allowed coordinate transformations of secular coordinate transformations which take the whole expanse of space and time and simply squash a bike warned the transformation finite regional bloc for what you get is called Penrose Byron was a rule and the really is however you jeweler Penrose diagram basically only fools the 1st thing is you lose coordinates circuits or whole thing on the finite blackboard squishy squash if they get blackboard but subject of the rule of light radially going right always move a 45 degree angles this can be done for a very large variety of geometries but you can't squish advanced questions abound in such a way that the white race continued to move 45 degrees result of called Penrose diagrams then stole a mother mathematics of high you derive the particularly those diagram just want to read them Castille read bizarre looks like his other Penrose diagram of flats bracelets like this time access but doesn't go from minus an affiliate of Boston while it does not withdraw Hall of Fame between some point in the past some point in the future and that's the whole time axis the space access also goes out to some pouring vast really are equals infinity Arroyo equals infinity squash the rest of it is just a triangle in here there's let's see if we can take this grid In reply will run he stopped I want to weigh our war that he goes era and work your way out for years growing was 1 user Oracle's total coaster 3 without a cloud of infinite number of them in the year through a crowd up like that likewise would take time 1 and they get a crowd opposite appear in what was down here but strike Turin is great Thai Michael lines vertical time acquiring although opted time infinity that's less time to be all these vertical lines for gliders but warned more and more of them are here what about the horizontal lines they all go out to roll equals infinity that's all over here all the score starch Moshe don't point Rivera Russia but but courage OK about light rays
particularly light razor 18th from far away for the origins of light rays coming and from 1st of all in more 145 deg lines and the incoming wiry would require grass that would be the image in this diagram of raw ivory which came in like bounces off the origin and roars back out you could have earlier rays came in earlier announced factory all I erased all the incoming right originated on this side of the triangle now that's really way way out there and interview weighed down here all outgoing light rays past our on the diagram of here that's just asymptotically far away in that direction what about all the time like offerings time like lines of these observers for example people were standing still might be moving a little bit they all lined up up here where they come from a conference here if you walk out care but if you imagined moving outward along 1 of these timelines the larger and larger role you eventually get over years this diagram at Bagram harvesting diagrams this was just watch your score story of your favorite word is so that all be drawn on the blackboard was subject to a constraint speed of light stays were libraries 45 degree angles this is good Penrose the simplest Penrose diagrams and that's always our wealth say about this particularly those warship choirs of squares what all we're far cast those where's yard is this fall's passing the course for those who like her I suppose it would be if authority I suppose it would be if we drew accurately yards accurately it would be stroke passing through corners here right although . 90 degrees on 1 0 light raid that was point did not right at the origin of Misty origin How will would too if come back here for drug still before us Greece so this is a hard blow not now in this is the Argentina never gets yard so it comes in with a very very far away it looks like it's aimed straight for the the origins of books follows as but it doesn't quite get 3 origin comes in for the distance of closest approach and they goes back out so factor would look like we get to a distance of closest approach and then goes back out but of course is angles Amal was mountain saying the same direction the and promised Byram right to thing here a array about misses the origin just simply mess is never quite gets to red to get to a distance of closest approach over here and there was no word Yosef radio white raves I draw a 45 degree radial libraries forms which are deemed the radio right warns which I'm not radio you have to worry about specially they were recount OK these different places with different extreme limits of the Penrose Byram's have named of course this is just the climaxes the swamp here is called future time like infinity the Mariners usually just called she lost for wasn't very Fiat are just few of this 1 down here is called vehicles Myerson fairy time might Pestone affinity my future affinity for you coursework specify can vary so was me over here where are these remain Frost replaces where white raise come in from the cold white like Infinity was forms course past like like confetti this woes core future light like a to movie and for reasons that I have no idea this was originally labeled I'm minus minus past and for the future I was always labeled with a script by Grife crime right off might not mind notation soared there are apologize for it on courage to us Penrose Byron flat what about a black hole was a black or look like forget ghetto black hole let's really draw these diagram that we had earlier and then try this euro would look like if we did some smart shoes for sale for squeeze it onto a blackboard play has always are we saw a way out here space like Infinity that's way out a large distances from the black hole your Concorde moves like that here was a singularity or he was also a past singularity or he area and we did discuss foes on this side we did discuss what was on side I hesitated to tell you what was down here but eventually did what on assigned nothing of physical interest but nevertheless a mathematics all of which were chilled Bret contains all of its contains an outside world over year and another outside world over here the outside world was not the same as the outside world over here you can't get a message from here to here but the mathematics of show has both were fine hair from roosters really quite meaningless but for the moment this is what we found the metrical quite so With the geometry look like so let's ask what happens if we squishy rests the same kind of squeezing forget everything on the final play and an undisclosed brought for your show you what looks like you already know I think your recognize it pretty fast Mason guidelines the dual if Josh or a robbery in America OK let's start our here and equals infinity USITC articles filial U.S.-led war ARTS will you think it will adopt Qualia harsh this horizon over here a bifurcated horizon is right at the center over here saw at the horizon and go out I can go this right but I can also go along this line this is Ahmed equals 0 all made equals 1 wears out not assume leader case you want up so in the same place same place or you want them going out Oracle's articles and reviews Auburn North bank Bahia so will adult Nevada here
likewise from here that's a sequence of different hiring now let's look at different radial distances from the black hole therefore the radial distances change color different radial differences all these OR observers a few white course stationery outside the black or your time in Philly over here and they were partners in this guy is 200 miles the black or this was 500 miles black courts a thousand miles black at 10 thousand miles from the black or so forth swarm over here His hovering right above the horizon factor course is trying the hover above the horizon he must be accelerated the hover above the horizon takes on our rocket surgery keep going thrown out similar here but the other side is a perfect reflection of sorry and this I here that outside of a black hole as outside of a black or what's Bob wears you out here because are across the horizon wears horizon dressed why was the bicycle Verizon this is sort of a point of no return or he was a singularity vastly image are the singularity over here here we his In Your irate source warned take as the best singularity was very has nearly future singularity passed in your area this is a equals infinity way from white rays which come in come from here but now they don't bounce off the origin y happens to learn if a radially inward for Irish To Announce often go back out the now a form of black or passed through here where warned that a singularity their light rays which go out to infinity of course it could have been created by somebody worries these people here could have a flashlight and library out but they're also mathematical light rays which begin on a past singularity injury you out but but this is Corky cause infinity Aug . this is quality it was my innocence was called Oracle's affinity called past white like Infinity this is called Future large market Ferry this it that's a black hole at which would kill black always Archer Our drawn all of space time drawn on a piece of work real moving libraries always 45 degrees from this picture you could feel a lot of work of the properties of black holes were always talked about them already we talked about what happens when Alice Falls Bob stays outside his Bob is our success here hours of 4 times but the the flowers was moving more slowly but said what happened I want you cross into this triangle here's your door you have no choice but to go to the singularity now what is this region out here as seemed like a 2nd world who looks like a black hole the source of a lot of science fiction it looks like there are 2 worlds connected together by a black hole now formal art for all however it's not possible goal from this world this world because even a light wanted passes horizon went already so that completely out of communication with each other nobody on the side and Cindelyn aside so from the point of view of anybody in this diamond here this doesn't exist brought food glib wasn't the just doesn't exist in fact the real story is a little bit different the real story has to do with the way black holes on in nature this diagram doesn't tell you how was black or was made was black or so always there from remote from the remote past the remote future Ms. chilled metric workers mail a black hole which is eternal black also not made made by by collapsing star wars so the next question that we want understand is how is a black or maybe not a black hole before others a black hole is not completely empty space stuff was coming here we can imagine what's at stake of imaginary scenario some particles coming from very far away they might even be full when a no-fault arms calmly 2 regions on serve energy euphoria not photons and Masson therefore the gravitate if you get enough assault on energy into a region space you could make a black coal sorrow we'll start with now would not nothing always just a very diffuse clone of full commute from far away about practically empty space looks a lot like empty space where the diagram that represents a space as here that's empty space not black or just played empty space baby with some photons career after the photons comedy and if they make a black hole they later Will we should seize the black hole the question is is how do you put these together heavier put this together in the past with this in the future to represent the assembling of a block or so we wanna go I'm a little bit of current assembling a black hole to do so after value of Europe I think the furor mold for tonight will go through the construction next time but called her is Newtonian physics called Newton's theorem in general really it's called Burke cough syrup and very simple fact about Newtonian gravity or general it's easy to understand let's begin with 0 not prove that Our interferon not 1 of our squared forces one-off square forces can all our such as cool and force electromagnetism removed from me and the force of gravity laws squared forces could be described by lines of wars on just remind you of our lines of forests here is Massachusetts appointed past imagined lines of force coming out of it but was a force could also be full lines of a fluid coming out of radio coming out a source we are it could be dimensional with fluid spreading out over 2 dimensions water could be a three-dimensional sauce over here where fluid flows away from the source draw lines of forest fires of forest begin on the charged particle or the massive object just go out and they don't the domain of course on among amassed some players were charged RasterOps it was just 1 mass Baxter let's see what the
rules would be either electric field gravitational field rule areas at any point the gravitational field all I think I withdraw the gravitational wines pointing inward wires Yaakov's gravity attracts calling on things so rulers at any point force through a forest on a test object points along the direction of line of forest precious that point nor about the magnitude of a forced magnitude the gravitational field this proposal of density of a wife of you think of the space is being filled up with radio network of wines a closer are together stronger before a wines a forest the tour Majorie mathematical construction you folks place with his warnings of force all lines of formal flawed that Is everything that knowledgeable say about only infield gravitational field point object if you put 2 point objects and other religious and the fields which is exactly the same as saying I have 2 sources of flowing in this case I justice will be a stink of flawed because fluids flowing in your photos 6 of Florida a floor being Paul van and saw your heart through sources and you simply song in the field of both of them which means you study the flow of a fluid flow of the 2 sources Doc supporters right if you quirk out that you figure out the year yard field of arbitrary distribution massive now be no interference Vaughan was if I take a spherically symmetric distribution on man on a vigorous simple case shelled was more general veteran Missouri burned shelves rush-hour finish shall spherically symmetric mass areas you could think of every point on that show our role as producing fluid if you look on the inside of the shower there is no flow Ohio could there be which way with the flow floor inside the shell well you might say it flows radially by symmetry overflow radially but it was full side shall wear white Gul is no match at the center I'm assuming all over masses are Michelle does not place for the fluid buildup shrine there's no messages sent there they can be in radio for became beauty floral so the interior of a shell sources of fluid has no floor which is another way of saying no gravitational field all inside a spherical shell was not outside we are sorry as a fall which is really our word the lines of force look exactly as if they had emanated from the a point of the century and the total amount of flow is whenever the total amount of smoke coming out of shelters in the language of gravitation what it says is the gravitational field of a shell of him outside a shower absolutely identical to gravitational field of a point Mass the center but is either shows no gravitational field or so inside shell exactly the same as empty space outside show exactly the same service the point that there is a general relativity version reverse God incidentally history of this is truly even if the shell is time dependent for example as long as the total amount of food coming out of his users conserve the shell work to change societies in a way that did not change the total amount of fluid coming out with Todd who would still be true at any given instant gravitational field inside the shell would be that of empty space and the gravitational field outside will look exactly like point we just be the place where you go from outside inside which would change with time some particular a few have kind appendage shell mass which was contracted with a mass fixed outside its core you would see the point mass gravitational field inside you would see nothing only the boundary between the 2 regions will change with the same exact thing it is true in generative your almost the same calls my quite Croats sorely was the next time we will combine broadcast with these 2 diagrams and put together the fury of how black holes form so get Burke austere and remember it was it it's as if you have a stroke symmetric distribution mail where you see inside a spherical selected distribution just exactly what you would see if there was no matter flat space-time and be spaced flat car Minkowski whatever you want to call it just solution of gravity are vying Stein's theory with absolutely nothing there is grow empty space inside what about have see Tony gravitational field normal quarry where you think assuming outside that but there struggle mass but what the gravitational field on the outside Schwartz still another words the man on the inside is exactly that a flat space and the medic on outside is exactly that of the Schwartz You black hole we want with right on the inside we have world he squared minus the X squared why square feet square Money outside we have Ross Choi chilled arrive with metric Fassero courage war chilled write another large Keese together 2 things both of which we know very well connected together by a shell how not the massive Schwartz your solution short solution has a mass associated with it that's just the mass powerful shell was a mess social change over time even if it moves Eva fish are all contracts was a problem as of the show change with time when I was a positive value as both marriages and monitor the words E equals M C squared conservation of energy right may have a problem mass of pressure even if the can still change of course is shocked change their you build a suffers shall but the shows strong enough to maintain itself against the gravitational field what happens if starts the collapse as it collapses the man doesn't change but the radius of exchanges war was is I was just Rudolph flat space well was outside with short euros and b boundary between the 2 behaviors might change with time so a new next time is take a flat faces solution is side and Patchett together with me outside which is Swatzell social should have that and in that way we will learn in a very simple example how black holes for will find half of his Byram mean anything Bolcom what next time 0 formation of a black hole
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Metadaten

Formale Metadaten

Titel Topics in String Theory | Lecture 4
Serientitel Lecture Collection | Topics in String Theory
Teil 4
Anzahl der Teile 9
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15116
Herausgeber Stanford University
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract (January 31, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses on the geometry of a black hole near the horizon. He describes how standard concepts from quantum physics can explain the physics that occur at this point. In the last of course of this series, Leonard Susskind continues his exploration of string theory that attempts to reconcile quantum mechanics and general relativity. In particular, the course focuses on string theory with regard to important issues in contemporary physics.

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