Stability and Instability of Schwarzschild-AdS for the Nonlinear Einstein-Klein-Gordon System  

作　　者：Feng-Xia LIU Bo-Ling GUO 

机构地区：[1]Institute of Artificial Intelligence,Beihang University,Beijing 100083,China [2]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第4期778-812,共35页应用数学学报（英文版）

摘　　要：In this paper,we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon(NLEKG)system in the presence of a negative cosmological constant.We prove the well posedness of the NLEKG system in the Schwarzschild-AdS spacetimes and that the Schwarzschild-AdS spacetimes(the trivial black hole solutions of the EKG system for whichφ=0 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 SchwarzschildAdS spacetime.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.

关 键 词：nonlinear-Einstein-Klein-Gordon equation schwarzschild-AdS spacetime well-posedness bootstrap 

分 类 号：O175[理学—数学]