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arXiv · 1512.08004

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

Peter Hintz·Andras Vasy
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Abstract

We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstr\"om-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.

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Peter Hintz, Andras Vasy. 2015-12-25. Analysis of linear waves near the Cauchy horizon of cosmological black holes. https://doi.org/10.1063/1.4996575

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