Stability of the expanding region of Kerr-de Sitter spacetimes and smoothness at the conformal boundary
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917785232211968 |
|---|---|
| author | Hintz, Peter Vasy, András |
| author_facet | Hintz, Peter Vasy, András |
| contents | We give a new proof of the recent result by Fournodavlos-Schlue on the nonlinear stability of the expanding region of Kerr-de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Our gauge is a modification of a generalized harmonic gauge introduced by Ringström in which the asymptotic analysis becomes particularly simple. Due to the hyperbolic character of our gauge, our stability result is local near points on the conformal boundary. We show furthermore that, in yet another gauge, the conformally rescaled metric is smooth down to the future conformal boundary, with the coefficients of its Fefferman-Graham type asymptotic expansion featuring a mild singularity at future timelike infinity of the black hole. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the expanding region of Kerr-de Sitter spacetimes and smoothness at the conformal boundary Hintz, Peter Vasy, András General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry Primary: 83C05, 35B35. Secondary: 35C20, 35L05 We give a new proof of the recent result by Fournodavlos-Schlue on the nonlinear stability of the expanding region of Kerr-de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Our gauge is a modification of a generalized harmonic gauge introduced by Ringström in which the asymptotic analysis becomes particularly simple. Due to the hyperbolic character of our gauge, our stability result is local near points on the conformal boundary. We show furthermore that, in yet another gauge, the conformally rescaled metric is smooth down to the future conformal boundary, with the coefficients of its Fefferman-Graham type asymptotic expansion featuring a mild singularity at future timelike infinity of the black hole. |
| title | Stability of the expanding region of Kerr-de Sitter spacetimes and smoothness at the conformal boundary |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry Primary: 83C05, 35B35. Secondary: 35C20, 35L05 |
| url | https://arxiv.org/abs/2409.15460 |