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

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 i...

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Veröffentlicht in:Journal of mathematical physics 2017-08, Vol.58 (8), p.1
Hauptverfasser: Hintz, Peter, Vasy, András
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description 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.
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source American Institute of Physics (AIP) Journals; Alma/SFX Local Collection
subjects Black holes
Cauchy problems
Cosmology
Decay rate
Physics
Red shift
Regularity
Scattering
Wave equations
Waves
title Analysis of linear waves near the Cauchy horizon of cosmological black holes
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