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Register a new userNear-$AdS_2$ perturbations and the connection with near-extreme Reissner-Nordstrom
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Added by
Achilleas Porfyriadis
Publication date
2018
fields
Physics
and research's language is
English
Authors
Achilleas P. Porfyriadis
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The geometry very near the horizon of a near-extreme Reissner-Nordstrom black hole is described by the direct product of a near-$AdS_2$ spacetime with a two-sphere. While near-$AdS_2$ is locally diffeomorphic to $AdS_2$ 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 $AdS_2times S^2$ and the associated connection problem with extreme Reissner-Nordstrom. In this paper, we give the solution for perturbations of near-$AdS_2times S^2$ 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.
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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 $AdS_2times S^2$ in Einstein-Maxwell theory. On the other hand, $AdS_2times S^2$ 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 $AdS_2times S^2$ 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 $AdS_2times S^2$ 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.
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