Reissner-Nordstrøm-de Sitter Manifold : Photon Sphere and Maximal Analytic Extension

Abstract

This paper is devoted to the study of the Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacetimes. Here, we find the necessary and sufficient conditions on the parameters of the Reissner-Nordstrøm-de Sitter metric -namely, the mass, the charge, and the cosmological constant- to have three horizons. Under this conditions, we prove that there is only one photon sphere and we locate it. We then give a detailed construction of the maximal analytic extension of the Reissner-Nordstrøm-de Sitter manifold in the case of three horizons.

28 pages

References in corpus (3)

• Relativistic images of Schwarzschild black hole lensing
• Strong gravitational lensing --- A probe for extra dimensions and Kalb-Ramond field
• Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited

Cited by in corpus (10)

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• Conformal Scattering of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Hole Spacetimes
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• Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity
• Decay of the Local Energy for the Charged Klein-Gordon Equation in the Exterior De Sitter-Reissner-Nordström Spacetime
• Scattering theory for Dirac fields inside a Reissner-Nordström-type black hole
• Light from Reissner-Nordstrom-de Sitter black holes
• A new type of charged black hole bomb
• Decay of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Holes
• On the Scattering of Waves inside Charged Spherically Symmetric Black Holes