Reissner–Nordstrøm–de Sitter manifold: photon sphere and maximal analytic extension

Abstract

This paper is devoted to the study of Reissner–Nordstrøm–de Sitter black holes and their maximal analytic extensions. 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 these 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. Studying these properties lays the groundwork for obtaining (in separate papers) decay results (Mokdad 2017 Decay of Maxwell fields on Reissner–Nordstrøm–de Sitter black holes (arXiv:1704.06441)) and constructing conformal scattering theories for test fields on such spacetimes (Mokdad 2017 Conformal scattering of Maxwell fields on Reissner–Nordstrøm–de Sitter black hole spacetimes (arXiv:1706.06993)).