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General Relativity | Lecture 8

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Stecher University OK the
last time I explained to you cross got niche for black
coal the school over it and tonight I want to show you how you could think about the formation of a cycle real black hole and how much Of this cross golf story diagram we joined the black on black rest time really is physically meaningful not all of it is a case of a less time to show you that the geometry of the metric of a black hole the shortage of black hole has the property that very near the horizon the horizon over it looks like flat space on the horizon is a kind of pull cordoned off hyperbolic polar coordinates pouring similar to the behavior I accelerated coordinate frames somebody standing outside and his wedge over quadrant over here is outside the rule is 1st of all a 45 degree angles represent the motion of light readies Europe only in that direction of misdirection somebody outside the black hole means out here quadrant of label quite earned 1 . 2 Cordiant 3 quadrant 4 as a gone Quattrone 3 and quadrant for really don't have any physical significance were real black coal quadrant 1 and quadrant tool which have real significant outside the black or somebody at rest outside the black call somebody arrest of course is experiencing the scent of acceleration just as I'm experiencing the acceleration our right here have gotten used to it so modest effect that OMB accelerated but there from somebody who would be out of space too long free fall to longer lost the of were gravitational field was is like a new plant them on the surface of the earth they would be experiencing the sense of awkward acceleration and in fact his diagram somebody arrest does appear to be accelerating away from the horizon commit single out and it's that acceleration which is what we experienced as gravitational acceleration near surface of the earth but in this case near B horizon of the
black or so this is not a family of 4 observers further and further How would very far from the black hole warehouse yes even close to a horizon here the closer you get on the horizon the more you'll have to accelerate curvature of these lines the more you have to accelerate to keep out of the black hole in case this is the exterior the lines of constant time it look like this red lines are lines of constant position the green lines all lines of constant trying them and they accumulate up near was blue line up here so people 0 equals 1 vehicles 2 0 2 3 and people's infinity is way way up on 45 degrees so that's the outside of the black hole on the inside of a black hole is quite No. 2 8 quarters number tool for real black hole geometry enough flats space but for a real black hole geometry something nasty mess to use the singularity the singularity looks like there's a what looks like us and never seen a bad place with lots and lots of tidal force and the problem with his once you find yourself in quadrant to there's no way out the only way to get out even that much even if they they left even if quadrant 3 was meaningful which is not war meaningful you can't escape from here found orbital out here without exceeding the speed of light trajectory somewhere has have and at a direction which is shallower than 45 degrees and that means exceeding the speed of light so that means it exceed the speed of light the only place Xircom wind-up In some ways I'm singularity 2 on if outside when you make a bad mistake you go but if you don't make a mistake you could jump back out near our so people on the outside or light sources on the outside of flashlights review like they can produce signals which go in or they produce signals which go out and that's the character of black or a picture Veps tourist black calls the geometry is somewhat warped it's not just flat space that's somewhat warped and curved but is basically a public prime space Parliament's based as she by hand in a falling observer of the last time the position through what they should yes that's correct so for somebody falling in doesn't accelerate the coordinates of the which are not too too different from ordinary flat based in free fall at least until they get near the singularity find an ex those of a quorum such a person would you them the spacewalks flat pretty much pretty much especially near the horizon over here the somebody and outside the experiences acceleration acceleration is basically the same as the accelerated reference but OK now is very convenient very convenient to read draw pictures like us spaces in 50 here goes on and on and on and some mourners in the
next county forever and
our time may come to an end at the singularity over here but these directions author 45 degrees is like like directions that also included and so I can't draw off the entire space time on the blackboard many purposes it is EU full convenient provides some visual tools provide some intuition and be able to draw on higher space time refinery piece of a blackboard but it could legend why you wanna see everything that's going on you wanna get a complete overview of space time we like to draw on the blackboard by region let's start doing that but let's start with black but start with good old ordinary space and take all of flap space time rising space we like space time and let really draw a four-week warden at prices so that we do accorded transformation which pulls or whole fleeing into some finite region Austria do that on this is useful and Bentley of geometries space times which have rotational symmetry potential symmetry means that the same in every direction that mean the same thing rotational similar symmetry what we say a gravitational source as rotational symmetry in the same in every direction and what system is the same in every direction and have rotational symmetry it's usually useful to describe it not talk about ordinary poll course system as rotations of the treaty to saying that every direction we don't care so much about the angle everything the same independent of angle will we care about is how things vary as we move away from the center the radial direction and that sold Ferrer many many purposes we don't need to think too much about the angular direction we just think of space-time flat space-time would reflect time as having a Timex at the time access goes from minus infinity plus infinity and has a radial direction the radio direction is like that the radial direction never gets
native never negative in polar coordinates are always positive and Serbian they on it is still a right of the ecstasy C only cause being the left of the time axis would mean negative R & R was always positive it's the distance distance from the origin of his everything on the entire space time and left much but some markers on it To be visualized hours from landmarks 1st of all Wallace horizontal axis is equals 0 he equals 0 area as table 1 people long looks like this people still looks like best people's minus 1 was like best keeper stores like this and ever want to draw the entire said possible crimes with the take me up to to work with the head and damper health services for all possible crimes Italy could also plot all possible radial distances and the radial distances just look like they are 1 oracle's to Oracle's 3 a in cases I will imagine using units so that the speed of light is 1 sequels 1 simply means that our work in music will 2nd time use like seconds for dissidents and then light rays like rays will move a 45 degree angle well that's not quite right let's think about the motion of libraries if a light gray withdrawn picture of his Oracle 0 Is polar coordinates radius here just too 1 and the time looking In including the angle of if light gray radially for the origins it hits the origin and they want to do it goes back down a drug straight this just saying light gray in polar coordinates that happens to be directly at the origin from far away urgent coming in from very far away there happens to be a direct to the origin who will go to the origin mingle backed out of it and this diagram it will appear them back to reflect off the origin his articles Iraq Oracle 0 over here so I break coming in from Long in the past would look like a bigger views color Our lightweight coming in from the past will look like this a 45 degree angle it will get the origin at some time we get the origin it was simply stop backed out it hasn't really reflected off anything of course just gone through the origin and went back out sold a light gray start in the very remote past coming in a 45 degree angle from a place that we called like likened past life like below is the place where all light rays come from a new text and they go out to be the future of course there are other light rays do the same thing this 1 comes in a little bit earlier singles out a little bit earlier 1 here but they all look pretty much the same come 45 bounce off the origin and they go out of 45 that is fun let's think about a light rate which doesn't the origin of life which doesn't pass through the origin will miss the origin comes in and Mr. the art was very very far away he became really tell it isn't unless you have a very good precision angular position decision finding new precision watching that like already way way back there it's hard to tell whether the odds are not so if stocks coming in pretty much the same way but if to get to the fact it almost appears to be repelled away from the origin and go back down every policy is not rest real good posture and that is what we call and tropical forests it really is tropical forests Ave the keeps alive ready for original you could just say it doesn't the because it was being the origin same thing but was look like it comes in pretty much the same way at 1st and instead of going through the origin it gets point of closest approach the closest approach over here and at at that point because about going back down so I like Ray which is perfectly radially tool that hit the origin of 45 reader our of both in going about going line but a library which misses the origin looks like in fact so the below the of a road like us just tell you these things here could use a million marks to give his perspective on what to do next next work take this diagrams and with squeeze it stretch in various ways to get a hold on the black that's good for me look the same but not until a 1 thing 6 1 thing fixed that light rays will always be assumed 45 degrees in of awards will be squeezing squashing stretching that we do do should preserve the fact that light rays moving 45 degree angles at a useful thing bill because we could see how raised more we can see what's going faster than the speed of light going slower speed what looks like so much I had that's not a bad thing got black no no not moment is nothing special just that particular point that we may want to focus on there may be some forget but that no need for it that is the got that the joys of coordinates Vermont now but may be good physical reasons to want to use a particular choice support our own studying the sun and there is no black hole bar does symmetry of the problem makes it convenient to think about the son being sent there of something right that's order of white next step let's assigned midsummer the coast he did not recall vertical axis capital capital city and the horizontal axis capital are don't confuse them all with others he's an aura of going to use that we have been using some of the core capital P capital but there is another way to coordinate ties and that's Silas coordinates at 45 degrees words introduce actually is all 45 degree angles here and here Of course I don't mean to imply that there's anything behind Oracle 0 hour were only interested in this region here but we introduce new Courtnage end this quarter here that's not good are it's going to be T plus he plots ah varies as you go from here here here if I were the plot constant peoples are constantly plus would be line what I draw well budge
drummer picture over here are key constant T plus are we look like this is a bigger lines of constant P Plus are the focus of his people are thought he had he not far from here on Tuesday song alone he might fall he's a useful for a seat he might ah is called T minus just as you might expect OK so we have a different way of describing the scene space-time missing flat go flat space-time instead of C plus are and where we have people and he might now what about this line year this what was this line this line was just plain or equals 0 are equal 0 so what is that what 0 that's T plus equals he might strike people a sequels stigmata state plus Eagles minus as the same thing as he plots an because he minors are or our Eagles minors are the only solution Oracle's miners oratorical 0 so this final this year which was articles is also just keep plus equals costing ideas at a way to describe it OK now change and the way with a change coordinates is to introduced 2 normal more difficult like like like quarter was called like like war to change like like coordinates were going to introduce tool no like like war 1 of them is called you plus 1 of them is called you minus a new blasts is a function of steep losses so you plus some function of T class it's not going to involve minors a new minors is going to be in fact I think the same function of key might this function Mrs. coordinate transformation it which you plus and you might as independent Ostreidae pleasant T minus just independently transformed milk war now but what kind of functional going to use I'm going to use a function also keep plus as or you will persuade you equals F of plus and the function as look like best when you go out to keep at it doesn't ever become absolutely flat it's always got a slight positive also Barron here also has a slight but it will go toward already yeah you plus new plus so plants plus of infinity is 1 parent or just ask Corvette F of infinity is worn and Efram minus infinity is 1 Miller anybody not function that does that them many functions would do that Ford died yeah hyperbolic tangent is the 1 that's usually you hyperbolic tangent 1 asymptotically it's the usual 1 that's used but does nothing special about a hyperbolic tangent hyperbolic urgent her F our people lost and if you don't know what a hyperbolic tangent don't worry about it it's just a function which like that pinch of people if OK now think about what happens as we start moving on this graph further and further how Ward keep plus is getting bigger and bigger and bigger ones you plus billing it's never really get bigger than 1 right it's never gonna get bigger than 1 so let's draw Our think they started with these nor cordon that erased a revert back our new plants equals hyperbolic tangent of people and same thing for my as we move out for 3 drop picture as we move out work started are start over here the move our how big those you plots you plus never gets bigger than 1 sold this diagram office's BU planes not be empty planes but you play you plus never gets bigger than 1 period is right there it never gets bigger than 1 so that means all of the space time has been mapped down what about you you might guess is Eagle Tool hyperbolic tangent of what this says is as we moved down In this direction team minus never gets bigger on less negative than like this 1 team minus is getting very very big and negative as you go down he is getting bigger and bigger but negative as you down here but you'll minus so Max's out again at minus 1 and him team minus equals minus 1 might never gets too far P plus never gets to far now I'm sorry I plus remind them of their foreign plus you plus 1 as you minus equal minus 1 fact what about this vertical lines year the original vertical line over here was people equals team miners rights keep plus equals T minus that's the same as Oracle's 0 50 plus equals remind that you plot equals you might say so in fact this line happens to be you plus equals you mind this and looks like a vertical line all we've done if you had don't follow the details always done squish the geometry this way squish the geometry that way and squish did aren't find triangle who understands better when I draw in these coordinates man off what is trajectory of a light gray outgoing but say a a outgoing like In terms of the key pluses and the minuses well now gone white it is in a constant value of which he minus guess he miners would be constant and fixed on here plus would be constant been fixed for normalized but he class is constant and fixed along some trajectory it
means that you plot is constant and fixed along trajectory likewise 59 Newman the upshot is that if you make the coordinate transformation like it is still true that radial light praised move on straight 45 degree angles as is ours light rays coming from read from the remote past bounced off the origin and go back out again bouncing off the origin is just a figure of speech you just passed through the origin so we succeeded in taking all space and mapping it to a triangle would enjoy the whole thing on blackboard let's go and some Court joined a detail in particular let's take these horizontal slices which correspond to different kinds of cement is starting at the origin but With people 0 August people 0 and moving outward outward outward will allow ourselves even exceed the speed of light and just move outward in arm adulation was at look like that of course looks like starting point over here and moving outward from and where you eventually get to you get there Seoul this point must be spatial infinity Oracle's and that's where you get to if you just walk along this line could you get out but what about the slide over here vehicles 1 if you plot that in these coordinates who started out of India but it will grow to the SINGAPORE likewise people's minus 1 so we've done is squish full of spatial infinity with questionable point for every year and called space like in the both spread no then that that may not exactly straight depends of course on the particular choice of function but they won't be straight with more carefully 1 of them will be straight 1 be strength will be people 0 this 1 will be straight then the next 1 will look like they're still have some curvature what about where Haley way up there pulls a hundred billiard tables are 100 billion is going to be very close to the edge so as we keep putting in more of these accumulating closer and closer to the edge of you gotta get infinite number of the act I'm really does go on and on forever at least flat space and so this is what these series hiding lines would look like different kinds of the other hand there let's look at fixed spatial position fixed spatial position can mark off different locations his Oracle's 1 news articles to Oracle's 3 articles for Oracle's 5 . about Megan goal squish near Oracle's where do they all go all gold vertically upward and on this diagram they all go up right up to this point of view checked back are doing a transformation and that's what you would say more and more more of the same diagram just in different coordinates and this coordinators said Everything gets fight a region space again emphasize or light rays 44 radio light weighs more 45 degrees they come in and they go out and so forth OK this called this process of squeezing everything aren't will find a piece of the blackboard without changing the speed of light it's called compact affrication think everything new compact of fire it but also called making up Penrose diagram misses append those diagram of flat space time Roger Penrose sometimes the core Carter Penrose diagram because high physicist named Carter think actually invented 1st Britain's Carter but usually called arms dirt so that's flat space-time laid out on the blackboard now the question is supposing you took the black hole is a black hole geometry they also go let's put it this means of point this is called spatial infinity or Oracle's this will not appeal would you call at the Soviet when you just go vertically upward that's kind equals infinity terms that use green people sincerity at the point where just 1 that's tables Midas in February Cox acts of this I'll give this is called a future time like Infinity misses called past time like infinity this is called spatial infinity or space like about these lines he is hardly is 45 degree angles is 45 degree angles aware of all light rays come from like arrays coming in and go out there and I go out because it takes an incident at the time and to get out for light ready beginning infinite remote past starts out its life coming in a longer 1 of these like like trajectories year bounces often goes back out the standard terminology used to call his script are minor sometimes called described script by ideas
while I'm away I came from an auto customized means this score last script by plus and these are called past like like infinity and future like like in a place where the place where a rare light rays begins and the place where light raising and that's the terminology calm not sourced reflects based looks like when compact defied now what about the black hole which watch a black hole orders that look like can't do exactly the same thing to do exactly the same thing at this whole diagram introduced again I guess we could call on Capitol are our original Chris golf coordinates we again introduce like like coordinates people are Sorrentino do exactly the same operation while we get what it will look like draw over here and that Australia how works tough look at everything and the whole thing hour on the final black and I think you'll probably see what goes where the exterior of the black hole that this quadrant over here the Square square of from probably end up we can again draw drawn quarter his people 0 here's people won his vehicles to 3 form that corresponds to these are wines which all passed through this point over here they also passed this point over here the origin over here which is the horizon is right over here OK what about the vertical lines the Red River the red vertical lines was a constant position foes observers were hovering above the black hole a constant radius the way out in further out further closer there is somebody hovering close to the horizon here Sunday hovering very close to the horizon the closely Holocaust the horizon the more you have to accelerate to keep out comfortable thing be home hovering above the euro Verizon because you've been pulled jerk but whatever we're being accelerated this is the X theory of a black hole what about quadrant to quadrant over here quarters tours over here and it is a place where your daughter is a singularity novice singularity is not often infinity it takes finite amount the proper time the fall from the horizon the singularity of finite excursion from here here so the singularity is a finite time always somebody you falls through doesn't get to experience an infinite time they will hit the singularity and that curative all the hole black hole geometry laid out and banners diagram if you're over here you doomed yet you can escape while you may going that you should ask yourself now what is this other here this is the outside of the black hole What is this other half over here and what stems here what's that here particular was this thing I drew down here that's quadrant 3 key in quadrant 4 quadrant 3 and quadrant 4 have no real meanings are already real physical black hole with the city will work out a real physical black hole but they really have no meaning they not really on the diagram of real black nevertheless nevertheless you could ask what kind of geometry is described by this full call what's called extended because golf diagram it seems that have to lay exterior region of the things that have to lay exterior regions a 2nd exterior region over here where you can escape outward in this direction or even fallen from side that seems to experience regions connected together at the horizon as the horizon that's the place where aura is equal to toe injury are equals 2 and G. Schwartz remember it's a place where 1 minus 2 NGO Va change sign as you came in you suddenly change signed and went off a like like correction but so that's a that's where looks like but supposing now Wheat take slice he looks like grew through from here to here what does that face like its base subspace time space on his green sliced green sheet surface was a look like and looks like you start that way out here is that our way out here in space is very big they the celestial sphere is very big way way half-year far so that is very big regional suspects is drawing it as a place as you come in you moving closer and closer to the horizon what happens to the radius of the of the sphere it shrinks down Oracle's to so it could make could run it's getting smaller and smaller the snobbery good award for as but look almost a John
but as we commend shrinks down he circles OK let's go back a 2nd each point on this diagram represents two-dimensional steered to understand why a representative ritual sphere remember we use in full accord right so just and polar coordinates are plain each radial distance represents a circle each radial distances in polar 3 dimensional polar coordinates represents a spear each point here this is fear that somebody could move around on two-dimensional sphere and the two-dimensional sphere is very big way out here as you come in the two-dimensional sphere gets smaller and smaller Aunt Tillie gets some minimum size over here and that's the horizon of Oracle's toe injury well what happens if you just keep going on the diagram sort of fake diagram half of which has no real meaning that will say well at start expanding out again start expanding out again until it gets very big it looks like you compare yes the rule from 1 side to the other by going through what people call word at it's also called Einstein Rosen bridge that connects cool what appeared to be X-terminal regions of black hole which had bigger and bigger and bigger as you move away from it and it looks like the black holes connecting to work to universe 2 asymptotic region as you might think well you go past from here here it can let's think about somebody who wants to start on the side and once the past size of this start here anyway is on the side and they want to pass to the size of the trajectory has to exceed the speed of light is no way to get from this quadrant that quadrant even if you start very very long in the past and you're willing together go way up into the future you still have to exceed the speed of light so in fact this diagram a little bit misleading it's everything in an instant the time but there simply isn't really kind to go from 1 side or the other you cannot go from 1 side to the other and the Einstein Rosen bridge is not really a bridge 1 later think about it Is that opens up encloses again before and I think passed through it but that's where the think about this just look at the figures and say if you could exceed the speed of light and moved horizontally yes you would move from year to year and going through the neck at the center but they are not allowed to to do that you could only move on 45 degree angles or less and you really can't get from 1 side to the other this has been a source of firms also teach science fiction passing from a from 1 universe to another through the center black hole because you could see the impact on these kind of wormhole sort of your call on which you cannot get through called month reversible warm holes mean to say you can't traverse and you can go from 1 side to the other and sorry to disappoint you prepare warriors but a fact as in a few minutes meaning of the left hand side there's no real meaning the left side anyway there's no place to go there is no real left inside the left hand side is the absence of let's talk about creating a black hole creating a black hole homeland laboratory that so far but creating a black hole infinite space by having some in falling matters and we're going to take a very special kind of informing them of the those a magic making a black always start with no black or is no black bowl we have is a very very distinct shell celestial made out of a fire in anything like that it's a shell of incoming radiation somebody way way far away created the incoming shell of radiation shelled Ava radiation radiation carries energy radiation Kerry's momentum and the show's coming coming in with the speed of light at some point as we will see this shell gets close enough together so much energy a small region that a black hole this is the simplest version of black hole formation our star isn't really made up ever things which formed with the speed of light this is the problem of a black hole being formed by stuff coming in with the speed of light on a thin shell is the simplest of all our relatively problems selectively to figure out how works you need to know really only 1 important thing to look for the shell moves in with the speed of light and the other thing is a version of looked theorem debate known the as of gravity for spherically symmetric gravitational region In particular forests from mass distribution which forms a shell posing mass distribution which forms show it doesn't matter whether it's moving doing anything if you ever mess distribution which forms a shelf for which has nothing on the interior then there's no gravitational field on the Interior Interior is completely without gravitational field so if you have shell material spherically symmetric with nothing on the interior is a gravitational field outside Newtonian as a gravitational field outside which is I think to a gravitational field of a point massive saying the man on the inside of the show it was not so outside it looks like a point may inside it looks like there's nothing that's Gratz Newton's theorem or a special case of the the interior of a distribution of mass which forms a shallow you see no gravitational field army outside you see the gravitational field as it would be if all of that mass was concentrated point that even true 0 if the shell is moving at the show moves In more and more space will look like the field of the point man and less and less will look like a empty space but interior to the shell and always looked like nothing their exterior to Michelle point this year is also true in general relativity the statement of the pyramid is if you have a shell In falling or show of mass of any kind then the interior region is just flat space time just as if it was no source be exterior region it doesn't look like the Newtonian point source what was it look like it looks like the Schwartz chilled solution so if you have in general relativity on the inside of the shell of mass flat space-time flat space time and the of it it looks like the short show black hole 8 such black hole so if you
had a static nonmoving shelf what you would do it to construct the actual solution is as you would paste together an Interior here which was flat with an X exterior which was which is a short trip is to do the same thing Newtonian physics paste together no gravitational field army out on inside with standard gravitational point source on the outside and that's the way you find solutions of a Newtonian physics to do exactly the same thing in general OK so now we can but 3 drug arrest is black hole here for a minute put back raced for 2 more prepared but OK so let's go back up flat space-time in flat space-time embroidery I wanna get rid of all these decorations and just put in but nothing nothing but now I want to be at the idea of an incoming shell of radiation you could think of the incoming shell of radiation as a sort of pulse of incoming photon a pulse distributor nice mirror From incoming photons and this picture here they come from like like Infinity here's pulse of throw pulse of incoming photons arranged around Kabul delayed a little bit later here there's a pulse of incoming radiation performs a shelf where is the interior of the show at any given instant Where is the interior and where's the exterior of the shells so that's easy yes a line at constant prices space where is the interior of the shell the interior of the shell of an interior regions period to the shelf that's the part of the space time that inside the shell the Oracle 0 the part of the space time that's outside the shell is out beyond the blue line here out here is the incoming shall I was noticed theorem general relativity version of it say it says that only if Syria of the shelf wept everything in here everything in their flat space-time and other words correctly represented by the space time that we drew here which was just a representation of flat space-time a festival and the interior of the shells which is left here the of just the flat chain rose diagrams is the correct representation of everything that's going on right now about here out here we're told that gravitational field the gravitational field was not look like flat space-time so this region out here is wrong this is not the correct representation of of the physics of the geometry of the falling shelled out beyond the shell was a bright correct correct representation the correct representation is just what she'll black hole so let's redraw the short show black to get rid of all over you the 3 drug Thai George Herbert will dish of Pixar here is and now some money and the outside froze in the shelves show opened riding in was a book like that looks like that's used blow before well I was is here's the incoming shell comes in experiences nothing special at this point over here and just keeps going but eventually it and it's a light ray of light gray radially incoming light rays must move on a 45 degree angle moves in and just eventually hit singularity answer that's what the light we would look like on the short geometry but now which part of the diagram is correctly represent finger the physics that would do it the interior of the shell is not correctly represented by the barrier by Barbara by a black hole the interior of the shell is correctly represented by flat space-time see exterior which is correctly represent the exteriors out here we make a little bigger just a overriding means those slice of San Miguel bigger but is means Michelle starts in earlier the orange part here is the correct description of the space time of informed Shell and the interior in here is not correctly represented so how we put these 2 together I would put these 2 together In order to make a single geometry and it's pretty easy you just take the wrong part of this a throwaway when you take the wrong part of this missing you throw away and you take the tour right parts and sold them together will move them together along joining aligned with begin falling shall take this put up there Re drawdown and it looks like this Brooks we could see what's going on right to say have taken this diagram always yes and Sept with placed it on top of the flat space-time drawn from the shelves matches across the shell a thing they have in common with the informed shows the region that the 2 of them have in common and on 1 side you plaster the CEO of black hole geometry and the other side you put in the flat space geometry that is the geometry of a black holes that was formed by uniformed excuse me Warwick consult with note that any questions about this get a Shell said late last visited is thought would also us but is not not discontinuity Broder but that where it at not nothing special happened but look at where the horizon where is the point of no return wear on the diagrams somebody do what you do is you start up and that corner that's the corner where the singularity abused me described lost the same thoroughly far away so don't worry about glad plus very very far away very rarely time but now a run off 45 degree line from there now it's not a place where anybody gets hurt if they fall through it it's just a place where you
don't fall through it you cannot escape from the singularity you will have a singularity Johnny outside of he you could get away you can escape described plus for example but notice something very very curious even over here you're doing this gone flat space-time is still on flat space b shall hasn't even gotten in yet you can't see the shell of you look backward on your like colonial Nazi the shell the shell is coming in that it would be the white light hasn't gotten to you yet you don't know the show's coming in yet if you're standing over here murmurs if you were somebody who was just falling over here the free fall your already behind the horizon even the Michelle hasn't even gotten in India you're still in flat space-time not only don't you feel anything drastic you don't feel anything nothing coming at you but nevertheless you don't you don't you can get out so the horizon extend all the ways back here was a game of course itself but soldier it is a sad Verizon toward the right who has collapsed as result when the show was glad with a 3 years William now right over here it is where the show crosses the photo latest fructose auto back draw picture firms is incoming shells has a certain amount of maps associated with that mass is sure to Radius products or some massive shell mess meaning energy is made of light but still has imaging and here Is the Schwab killed radius of a black hole with that if we had a black hole Of that it would have a short you'll radius of that it was always a mess is only outside well we can say that we masses on the outside of the tourist site but once the mass wants to a white crosses past the shore children years which extract it cannot get out it has formed the black hole for sure with his performance here OK right over here is informing it crosses the horizon right over here and then it's on the inside and there's no way for that chilled to change its mind we get back out our the shelter changes mind accelerate back out well I suppose shelves can't don't have minds but if they have a mind the times could turn around here once said it best here they cannot turn around begin tried a turn-around Mayorga very far the singularity so this is the point at which the shell courses atone for children if it the right half of the definition of the horizon is a place which seperate those people who can get out from those people get the case for collapsed chilled Ross the it is not lot better if you're already at show has crossed when he made before Baker prank quarters that you're doomed by the less repetition what more than like Rios by the time you get year Michel over trapping Gilly answers look at this diagram you look at the diary From a try to get out but by the time you got our fertile you can't get out you simply can't get out there you have to exceed the speed of light with diagrams the whole story there there's no more stuff if you hear you can't get out here you can't get out so the horizon has materialized before him before the shelter has actually got the yard into which which were the pair about it Shell let's face that editors what William walk is walking walking you walk away then you walk to walking with the speed of light is pretty fast walking there's a lot of weight right we are entered in there and it will that stated if Nova of here and that like children in a way that no of later filed but that when right leader or that killed while class enough to get out to get together with the that life is coming in at you you may be trapped even know you don't know the right rate from your Charles de proof is leaders with his fears of diagram of how you look at radiation it better call but it's radiation coming toward us now but we better that riot analogous but with a different analogy but that's that's not a shell coming as much committee the bird dumb OK so the horizon is a funny thing it actually forms before the material gets past a of radius and definition is it's point of no return to is point which appear on the side of it kick out of here on the side became points out for a year 4 of coal not so there was a meter right outside with election if are not what what well not likely you go really do this on is saying supposing that was a mirror right out right outside here I think the point is you can't have a barrier that has no weight if you got now Shirley you could do this to some extent you could build a mirror around the region like theirs and like Ray would reflect off a few really succeeded in building a the library would reflect off and it would be better the I'm like that now that the guy who wouldn't dare you would have a black hole so we we can draw on here he is a mirror and there is a certain distance away from the horizon away from the center is light comes in go free if who bounces off that'll happen not so much do not for and Joss this
light could decide turn around at this point there is no way that this gentleman over here could Callao light to turn around over there and not only can't resolve here became get the material out from over here he could try economy mirror the press he could have made America in the past and protected and allow Watson can yeah maybe so there was only a coming in he did decide to shoot out of Iraq and have that satellite really reflect there over there but once you get past the point once get past that point he cannot chewed out the mirror up to to this point he can't get out there is no time to rescue shelf Of course practice you wouldn't even know that that the light Ray was communion by might know you might know on you might have Bob could be we get ourselves the 1 who always goes black or not it's just at it's a convention writing it goes in the black hole but up till this point over here she's together with Bob the having a conversation and she tells Bob luck I got an idea I want you to go out there and then shooting in shelf and this is going to go off on a mini get trapped behind the horizon violated the singularity and fact I know that that's gonna happen even before I can see this show coming at me so it isn't that interesting so she could arrange with Bob contrived to send in shall know all that it was coming be over here but once you get over there too late for do anything about it she can't get the a Amira out they she get mayor here but getting over here is no good everything's behind the horizon a ready for anything back you with this singularity just gotta get the mirror around he can sell but it you're in that but the saying it has the gap Romero just a singularity where is 3rd another thing which is normal life structure not a work you could build a structure over here what's structure here which way chum reflected light so coming in he would better structure reflect and going through the singularity lira Alice light of it warns of funds in your area see there actually timers no it's not it's not something following is a finite amount the proper tie between here and here but the corner there is infinitely far away all but only the court on corn right but the implication is that somebody falling through the horizon has a finite amount of time survived well they could try to accelerate like once they pass the horizon Olivia interests same themselves by by sticking to that corner the problem with that is that it would take an infinite amount of acceleration in amount of energy to and make that much of acceleration the basically have to accelerate to soak up the speed of light or once you cross there the door but you could last a long time if you could accelerate are actually that doesn't work the ball you accelerate the less time you experience at the time was a war or better yet he did not think that the best strategies this can still exist except if they if now is the nature and extent of theirs don't that is why lost what they now that it's going to be that way your bread and other violent side but for which I am I'm sorry registered it not as a side by side in such shell that shot or at work and then I thought now we all owe you sorry you're inside filled before the shell crosses when you then father well yeah you could hang out with the show posture not assured sharp drop but I shell might keep doing makes management there but that's a that's a separate issue is translated into worrying for this being allocated you together watertight time where that that's a point in China this is a point of turned respect would some point of time would relate that distance from the shell that arise greater the right to person between us that differ we're looking at this picture 3rd how accelerate the eventual that arise get shot on price soared let's let's Esther but what the relationship between these pictures are part of charm emission drug that strut figures power and step nor will we do over here forever here by peers up Penrose diagram for the formation of the black hole is the horizon he falling shelf but In shell hits right over here now your speak of an instant of time at which time the were you the court we could make coordinate transformation in the incident of time really means you pick a surface you pick a surface which is everywhere space flight you pick a surface a is another surface pretty together around various kinds of warnings his another surface and a series of services defined a time variable time is 1 value on here another anyone here another value on here the value or here if you follow the time at this time he there's a shell faraway shows far away no horizon has formed yet at soros point not reached yet a little bit later the show is still a outside the horizon your inside and here this point over here that corresponds to the position of the shell and so far nothing has formed a means Bob this as a horizon over here there's a horizon at this point right over here at that time right over there that's the time at which the show passes its own torture radius the time at which would that be but the show passes into the interior of the horizon is the horizon shop prices including Syria and once that happens it can't get out from the area whatsoever if this were shot which was large 0 0 yes our review cocky about
this yacht that Barak's office radius is by definition is always the same thing but the size of the horizon right at this point here the horizon starts effect high-rises stocks very small only if few in the right near the center here are you do if you're out you still get a chance to get away that corresponds to being here or he the little tiny horizon has formed a little tiny horizon opened up during Hey have you dead if you're out he got a chance right same thing here if you're in here today that if after a year without the without the shell heavily even got to Europe the horizon stops to expand 1 killed you get to this point over here at that point the show for answers at that point the incoming shells crosses the growing horizon and past that pouring the shell was inside the horizon was on the outside and good now start doing what he was like a thought the dust-up Rory it stopped growing right at that port will others at will look up 88 my Yap this is a constant radius line that's correct the look like a bird observers say there worshippers we are stationary he also wrote on however that some Web some pointed does crosses were the horizon half Schweiger radius and the cost of the but what the you have experience only gravity courses show could have less is that is not dead yet is not dead yet nevertheless it's too late for him to escape red costing the horizon it does not mean that you sent me sudden gravity take place it only happens when you cross the shell but when you cross the horizon you know what that means that means you simply don't get away so now since the horizon is a little bit ghostly you that doesn't have a mercurial of significant weight shelled mom Murray falling through it doesn't experience that found via somebody falling through with that of his nothing there but flat Benes nevertheless nevertheless from that pouring cannot travel fast enough to escape the sack best shelves communion that they were removed that leadership role ever-rising Roberts that young that's right that's better from here from here you could escape from here you can't escape for this you're get a erect well yes yes yes yes yes yes but that's correct but you don't see any horizon opening up back yes that's right tractor after your have whoever you have you were best but there's a much simpler than hit to shells if the distance between observer leadership His the inner showed a rise in shell radiation shelter warehouse get-togethers can't get to that point work for us so please note that a much simpler way vision Idaho St 30 meters for what might break which I do a calculation that to find out where for example Verizon forms drive do that you find you find you can't do it the new warning that drawing pictures taking this line going backward to that point that's notorious corrupt by show you if you want to get good picture of what's going on the way to do it is to become familiar with these diagrams of if you try to reason our without a good picture in front of you that accurately represents the relationships between the the different parties and when the relations important relationship incidentally is not the relative size of here is a huge region of space and time this corner you to say they will circle here might be occurring in the region so diagrams are not correctly or your faithfully representing size what they represent their representing the motion of light and mother and in representing light breeze they're represent what things Our causal relationship target what what signals propagate cool could send a signal to a signal from here get from Allison here get the above out here it reflects the technical language would be that it reflects the causal structure cause and effect cause and effect means what can influence what a role as they can only influence the things in front of it where white can get to it cannot influence the things outside like all our souls these diagrams were hindered they would built 1st of all to be withdrew everything on the back a blackboard and 2nd of all to reflect faithfully the causal relations what causes and effects will consent signals the home of our who is trapped their stock having to go slow the speed of light both things are correctly reflected here and so for that reason these diagrams are very valuable I can't think about them I can't go if I have to answer a question of the kind you're asking I have to draw diagrams and diagram of says things much more clearly and trying the picture I can't do it a Super kids are guests with my guess is arrive came my guess is a writer wrong until a drummer diagram of they need to be told 1st well ought not Lord of war should play for warmth what what said 1 yet think edgy get but allocate the money mean this in these are at in a certain since these are abstract but you're right right there that that's that's absolute right general relativity is classical physics and to be represented it can be drawn could be even pictured to some extent by not so easy could draw a picture for four-dimensional curved spacetime but that's hard for 5 but still you go a lot further and visualizing yet been you can quite can think that's right it's an interesting fact choir mechanics is much more abstract OK Raquela's for more please visit us at
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Metadaten

Formale Metadaten

Titel General Relativity | Lecture 8
Serientitel Lecture Collection | General Relativity
Teil 8
Anzahl der Teile 10
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
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DOI 10.5446/15040
Herausgeber Stanford University
Erscheinungsjahr 2012
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract (November 12, 2012) Leonard Susskind develops the coordinate transformations used to create Penrose diagrams, and then uses them to describe the physics of black hole creation. This series is the fourth installment of a six-quarter series that explore the foundations of modern physics. In this quarter Susskind focuses on Einstein's General Theory of Relativity.

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