paper

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

arXiv:1512.08004 · doi:10.1063/1.4996575

Abstract

We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordström-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.

56 pages, 14 figures. v2 is the published version, with fewer typos and updated references

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