Strong Cosmic Censorship and Eigenvalue Repulsions for rotating de Sitter black holes in higher-dimensions

Abstract

It has been established that Christodoulou's formulation of Strong Cosmic Censorship (SCC) is violated by Reissner-Nordström-de Sitter black holes, but holds in four-dimensional Kerr-de Sitter black holes. We show that SCC is also respected by equal angular momenta (cohomogeneity-1) Myers-Perry-de Sitter (MP-dS) in odd $d\ge 5$ spacetime dimensions. This suggests that the preservation of SCC in rotating backgrounds might be a universal property of Einstein gravity and not limited to the d = 4 Kerr-dS background. As required to discuss SCC in de Sitter spacetimes, we also study important aspects of the scalar field quasinormal mode (QNM) spectra of MP-dS. In particular, we find eigenvalue repulsions similar to those recently observed in the QNM spectra of asymptotically flat Kerr-Newman black holes. For axisymmetric modes (i.e. with azimuthal quantum number m = 0) there are three distinct families of QNM (de Sitter, photon sphere and near-horizon). However, typically, for non-axisymmetric ($m\ne 0$) QNMs, we find that the entire spectra can be described by just two families of QNM (since several overtone sections of the photon sphere and near-horizon families merge). For completeness, we also study the full scalar field QNM spectra of higher-dimensional Schwarzschild-de Sitter black holes.

43 pages, 13 figures

References in corpus (14)

• Quasinormal modes and Strong Cosmic Censorship
• An instability of higher-dimensional rotating black holes
• The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit
• Instability of higher dimensional charged black holes in the de-Sitter world
• Branching of quasinormal modes for nearly extremal Kerr black holes
• Quasinormal modes of D-dimensional de Sitter spacetime
• Quantum BTZ black hole
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Strong Cosmic Censorship in higher-dimensional Reissner-Nordström-de Sitter spacetime
• Eigenvalue repulsions in the quasinormal spectra of the Kerr-Newman black hole
• Quantum stress tensor at the Cauchy horizon of Reissner-Nordström-deSitter spacetime
• The origin of the Reissner-Nordström de Sitter instability
• The renormalized charged scalar current in the Reissner-Nordström-de Sitter spacetime