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Entire spherically symmetric spacelike graphs with prescribed mean curvature function in Schwarzschild and Reissner–Nordström spacetimes

Daniel de la Fuente, Alfonso Romero, Pedro J Torres
2015 Classical and quantum gravity  
For each spacetime of a family of static spacetimes, we prove the existence of entire spherically symmetric spacelike graphs with prescribed mean curvature function. In particular, classical Schwarzschild and Reissner-Nordström spacetimes are considered. In both cases, the entire spacelike graph asymptotically approaches the event horizon. Spacelike graphs of constant mean curvature remain as a particular situation in the existence results, obtaining explicit expressions for the solutions. The
more » ... the solutions. The proof of the results is based on the analysis of the associated homogeneous Dirichlet problem on an Euclidean ball together with the obtention of a suitable bound for the lenght of the gradient of a solution which permits the prolongability to the whole space.
doi:10.1088/0264-9381/32/3/035018 fatcat:aaowx65cazd6hjisxy7kbawcpq