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This paper is devoted to the study of the Reissner-Nordstr{\o}m-de Sitterblack holes and their maximal analytic extensions. In particular, we study someof their properties that lays the groundwork for separate papers where weobtain decay results and construct conformal scattering theories for testfields on such spacetimes. Here, we find the necessary and sufficientconditions on the parameters of the Reissner-Nordstr{\o}m-de Sitter metric-namely, the mass, the charge, and the cosmological constant- to have threehorizons. Under this conditions, we prove that there is only one photon sphereand we locate it. We then give a detailed construction of the maximal analyticextension of the Reissner-Nordstr{\o}m-de Sitter manifold in the case of threehorizons.

Reissner-Nordstr{\o}m-de Sitter Manifold : Photon Sphere and Maximal Analytic Extension