Scattering of gravitational and electromagnetic waves off AdS2 × S2 in extreme Reissner-Nordstrom
- 52 Downloads
The direct product of two-dimensional anti-de Sitter spacetime with a two-sphere is an exact solution of four-dimensional Einstein-Maxwell theory without a cosmological constant. In this paper, we analytically solve the coupled gravitational and electromagnetic perturbation equations of AdS2 × S2 in Einstein-Maxwell theory. On the other hand, AdS2 × S2 also describes the near-horizon region of the extreme Reissner-Nordstrom (ERN) black hole. We therefore also solve the connection problem: we show how the AdS2 × S2 perturbation equations arise from an appropriate near-horizon approximation of the corresponding equations for the ERN and then, using matched asymptotic expansions, we analytically extend the AdS2 × S2 solutions away from the near-horizon region connecting them with solutions in the far asymptotically flat region. From the point of view of ERN our results may be thought of as computing the classical scattering matrix for gravitational and electromagnetic waves which probe the near-horizon region of the black hole.
Keywords2D Gravity AdS-CFT Correspondence Black Holes
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- S. Chandrasekhar, The mathematical theory of black holes, Clarendon Press, Oxford, England, (1985).Google Scholar
- A.A. Starobinsky, Amplification of waves reflected from a rotating “black hole”, Sov. Phys. JETP 37 (1973) 28 [Zh. Eksp. Teor. Fiz. 64 (1973) 48] [INSPIRE].
- S.A. Teukolsky and W.H. Press, Perturbations of a rotating black hole. III — Interaction of the hole with gravitational and electromagnet ic radiation, Astrophys. J. 193 (1974) 443 [INSPIRE].
- R. Fabbri, Electromagnetic and Gravitational Waves in the Background of a Reissner-Nordstrom Black Hole, Nuovo Cim. B 40 (1977) 311 [INSPIRE].
- F.J. Zerilli, Perturbation analysis for gravitational and electromagnetic radiation in a Reissner-Nordström geometry, Phys. Rev. D 9 (1974) 860 [INSPIRE].
- P.L. Chrzanowski and C.W. Misner, Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green’s functions, Phys. Rev. D 10 (1974) 1701 [INSPIRE].
- V.P. Frolov and I.D. Novikov, Black hole physics: Basic concepts and new developments, Kluwer Academic, Dodrecht, Netherlands, (1998).Google Scholar
- R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
- C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].