Stability and decay-rates for the five-dimensional Schwarzschild metric under biaxial perturbations
| dc.creator | Holzegel, G. | |
| dc.date | 2008-08-24 | |
| dc.date.accessioned | 2026-07-07T09:58:10Z | |
| dc.date.available | 2026-07-07T09:58:10Z | |
| dc.description | In this paper we prove the non-linear asymptotic stability of the five-dimensional Schwarzschild metric under biaxial vacuum perturbations. This is the statement that the evolution of (SU(2) x U(1))-symmetric vacuum perturbations of initial data for the five-dimensional Schwarzschild metric finally converges in a suitable sense to a member of the Schwarzschild family. It constitutes the first result proving the existence of non-stationary vacuum black holes arising from asymptotically flat initial data dynamically approaching a stationary solution. In fact, we show quantitative rates of approach. The proof relies on vectorfield multiplier estimates, which are used in conjunction with a bootstrap argument to establish polynomial decay rates for the radiation on the perturbed spacetime. Despite being applied here in a five-dimensional context, the techniques are quite robust and may admit applications to various four-dimensional stability problems. | |
| dc.identifier | https://arxiv.org/abs/0808.3246 | |
| dc.identifier | http://arxiv.org/abs/0808.3246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167620 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Stability and decay-rates for the five-dimensional Schwarzschild metric under biaxial perturbations | |
| dc.type | text |