Analysis of linear waves near the Cauchy horizon of cosmological black holes

被引:82
作者
Hintz, Peter [1 ]
Vasy, Andras [2 ]
机构
[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA
基金
美国国家科学基金会;
关键词
KERR-DE SITTER; MODE-STABILITY; PRICES LAW; EQUATION; SCHWARZSCHILD; SINGULARITIES; ASYMPTOTICS; INSTABILITY; DECAY; FIELD;
D O I
10.1063/1.4996575
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstrom-de Sitter and Kerr-de Sitter spacetimes and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon-which yields the boundedness statement-is a consequence of radial point estimates, which are microlocal manifestations of the blue-shift and red-shift effects. Published by AIP Publishing.
引用
收藏
页数:45
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