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arXiv · 1607.01018

Bounded energy waves on the black hole interior of Reissner-Nordstr\"om-de Sitter

João L. Costa·Anne T. Franzen
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Abstract

Motivated by the Strong Cosmic Censorship Conjecture, in the presence of a cosmological constant, we consider solutions of the scalar wave equation $\Box_g\phi=0$ on fixed subextremal Reissner--Nordstr\"om--de Sitter backgrounds $({\mathcal M}, g)$, without imposing symmetry assumptions on $\phi$. We provide a sufficient condition, in terms of surface gravities and a parameter for an exponential decaying Price law, for a local energy of the waves to remain bounded up to the Cauchy horizon. The energy we consider controls, in particular, regular transverse derivatives at the Cauchy horizon; this allows us to extend the solutions with bounded energy, to the Cauchy horizon, as functions in $C^0\cap H^1_{loc}$. Our results correspond to another manifestation of the potential breakdown of Strong Cosmic Censorship in the positive cosmological constant setting.

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BibTeXRIS

João L. Costa, Anne T. Franzen. 2016-07-04. Bounded energy waves on the black hole interior of Reissner-Nordstr\"om-de Sitter. https://doi.org/10.1007/s00023-017-0592-z

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