Stability of Schwarzschild-AdS for the spherically symmetric Einstein-Klein-Gordon system
arXiv:1103.3672 · doi:10.1007/s00220-012-1572-2
Abstract
In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. We prove that the Schwarzschild-AdS spacetimes (the trivial black hole solutions of the EKG system for which identically) are asymptotically stable: Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching a Schwarzschild-AdS spacetime. The main difficulties in the proof arise from the lack of monotonicity for the Hawking mass and the asymptotically AdS boundary conditions, which render even (part of) the orbital stability intricate. These issues are resolved in a bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained.
49 pages
References in corpus (5)
- Building an AdS/CFT superconductor
- Holographic superconductivity in M-Theory
- Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole
- Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes
- Self-gravitating Klein-Gordon fields in asymptotically Anti-de-Sitter spacetimes
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