Near-$Ad{S}_2$ perturbations and the connection with near-extreme Reissner-Nordstrom

Abstract

The geometry very near the horizon of a near-extreme Reissner-Nordstrom black hole is described by the direct product of a near-$Ad{S}_2$ spacetime with a two-sphere. While near-$Ad{S}_2$ is locally diffeomorphic to $Ad{S}_2$ the two connect differently with the asymptotically flat part of the geometry of (near-)extreme Reissner-Nordstrom. In previous work, we solved analytically the coupled gravitational and electromagnetic perturbation equations of $Ad{S}_2\times S^2$ and the associated connection problem with extreme Reissner-Nordstrom. In this paper, we give the solution for perturbations of near-$Ad{S}_2\times S^2$ and make the connection with near-extreme Reissner-Nordstrom. Our results here may also be thought of as computing the classical scattering matrix for gravitational and electromagnetic waves which probe the region very near the horizon of a highly charged spherically symmetric black hole.

14 pages, v2: Conclusion section added, Mathematica notebook attached, matches published version

References in corpus (2)

• Scattering of gravitational and electromagnetic waves off $Ad{S}_2\times S^2$ in extreme Reissner-Nordstrom
• Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole

Cited by in corpus (5)

• Extreme Black Hole Anabasis
• Gravitational Waves on Kerr Black Holes I: Reconstruction of Linearized Metric Perturbations
• Horizon Acoustics of the GHS Black Hole and the Spectrum of ${\mathrm{AdS}}_2$
• Near-extremal dynamics away from the horizon
• EFT Corrections to Charged Black Hole Quasinormal Modes