Bounded energy waves on the black hole interior of Reissner-Nordström-de Sitter

Abstract

Motivated by the Strong Cosmic Censorship Conjecture, in the presence of a cosmological constant, we consider solutions of the scalar wave equation ${\square }_g\varphi =0$ on fixed subextremal Reissner--Nordström--de Sitter backgrounds $(\mathcal{M},g)$, without imposing symmetry assumptions on $\varphi$. 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 $C^0\cap H_{loc}^1$. Our results correspond to another manifestation of the potential breakdown of Strong Cosmic Censorship in the positive cosmological constant setting.

21 pages, 5 figures

References in corpus (3)

• Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations
• Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
• On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion

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