Stability of Minkowski Space-time with a translation space-like Killing_vector field
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| Title | Stability of Minkowski Space-time with a translation space-like Killing_vector field |
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| Part Number | 5 |
| Number of Parts | 23 |
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| License | You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. |
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| Abstract | In the presence of a translation symmetry, the 3+1 vacuum Einstein equations reduce to the 2+1 Einstein equations with a scalar fi_eld. We work in generalised wave coordinates.
In this gauge Einstein equations can be written as a system of quasilinear quadratic wave equations. The main diffi_culty in proving global existence of solutions for small data is due to the weaker decay of free solutions to the wave equation in 2+1 dimensions, compared to 3+1 dimensions. This weak decay seems to be a deterrent for proving a stability result in the usual wave coordinates. In this talk we will present the construction of a suitable generalized wave gauge in which our system has a "cubic weak null structure",which allows for the proof of global existence. |
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