Stability of stationary-axisymmetric black holes in vacuum general relativity to axisymmetric electromagnetic perturbations

Abstract

We consider arbitrary stationary and axisymmetric black holes in general relativity in $(d+1)$ dimensions (with $d\ge 3$) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically deSitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes provided that the initial perturbation vanishes in a neighborhood of the horizon.

arXiv commentv2: Error in Remark 4.1 corrected; proof generalizes to positive rather than negative cosmological constant. v1: 24 pages, 1 figure

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• Stability of Black Holes and Black Branes
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Cited by in corpus (4)

• Angular momentum at null infinity in Einstein-Maxwell theory
• A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• Energy Extraction, or Lack Thereof