Near-$$AdS_2$$ AdS2 perturbations and the connection with near-extreme Reissner–Nordstrom

• Main Author: Achilleas P. Porfyriadis
• Format: Article
• Language: English
• Published: SpringerOpen 2019-10-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-019-7347-6

Abstract The geometry very near the horizon of a near-extreme Reissner–Nordstrom black hole is described by the direct product of a near-$$AdS_2$$ AdS2 spacetime with a two-sphere. While near-$$AdS_2$$ AdS2 is locally diffeomorphic to $$AdS_2$$ AdS2 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 $$AdS_2\times S^2$$ AdS2×S2 and the associated connection problem with extreme Reissner–Nordstrom. In this paper, we give the solution for perturbations of near-$$AdS_2\times S^2$$ AdS2×S2 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.