Black hole nonmodal linear stability: odd perturbations of Reissner-Nordström

Abstract

Following a program on black hole nonmodal linear stability initiated in Phys.\ Rev.\ Lett.\ {\bf 112} (2014) 191101, we study odd linear perturbations of the Einstein-Maxwell equations around a Reissner-Nordström (A)dS black hole. We show that all the gauge invariant information in the metric and Maxwell field perturbations is encoded in the spacetime scalars $\mathcal{F}=\delta (F_{\alpha \beta }^{\ast }{F}^{\alpha \beta })$ and $\mathcal{Q}=\delta (\frac{1}{48}{C}_{\alpha \beta \gamma \delta }^{\ast }{C}^{\alpha \beta \gamma \delta })$, where $C_{\alpha \beta \gamma \delta }$ is the Weyl tensor, $F_{\alpha \beta }$ the Maxwell field, a star denotes Hodge dual and $\delta$ means first order variation, and that the linearized Einstein-Maxwell equations are equivalent to a coupled system of wave equations for $\mathcal{F}$ and $\mathcal{Q}$. For nonnegative cosmological constant we prove that $\mathcal{F}$ and $\mathcal{Q}$ are pointwise bounded on the outer static region. The fields are shown to diverge as the Cauchy horizon is approached from the inner dynamical region, providing evidence supporting strong cosmic censorship. In the asymptotically AdS case the dynamics depends on the boundary condition at the conformal timelike boundary and there are instabilities if Robin boundary conditions are chosen.

Corrected treatment of axial perturbations. To appear in PRD

References in corpus (5)

• Instability of charged and rotating naked singularities
• Linear perturbations of self-gravitating spherically symmetric configurations
• A geometric description of Maxwell field in a Kerr spacetime
• Black hole nonmodal linear stability: the Schwarzschild (A)dS cases
• Instability of asymptotically anti de Sitter black holes under Robin conditions at the timelike boundary

Cited by in corpus (3)

• The linear stability of Reissner-Nordström spacetime: the full subextremal range
• The linear stability of Reissner-Nordström spacetime for small charge
• Black hole nonmodal linear stability: even perturbations in the Reissner-Nordström case