中国科学院数学与系统科学研究院
数学研究所
学术报告
广义相对论研讨班
Speaker: Olivier Graf （University of Grenoble, France）
Title: The linear stability of Schwarzschild-anti-de Sitter spacetimes
Time&Venue: 2024年11月21日（星期四） 16:30-17:30 腾讯会议：534-941-730
Abstract: Schwarzschild-adS spacetimes are stationary and spherically symmetric solutions to the Einstein equations with negative cosmological constant. They contain a black hole region and a conformal anti-de Sitter timelike boundary at infinity. In this talk I will present a result of linear stability for these spacetimes under gravitational perturbations preserving the anti-de Sitter boundary condition. As in the Schwarzschild case, the linearisation of the Einstein equations is governed by two Regge-Wheeler wave equations. I will show that the boundary conditions inherited by the Regge-Wheeler quantities can be decoupled into two boundary conditions: a Dirichlet boundary condition and a higher order ``Robin''-type boundary condition. I will show that these boundary conditions are conservative and yield to the decay of a coercive energy quantity. By red-shift and Carleman estimates for each spherical mode, one can obtain a 1/log(t) decay for the Regge-Wheeler quantities, which can further be infered for the full system of gravitational perturbations. I will also show how to construct quasimode solutions for the system of gravitational perturbations which prove that the these bounds are optimal. This is joint work with Gustav Holzegel.
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