Reduction of the n-dimensional static vacuum Einstein equation and generalized Schwarzschild solutions |
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Authors: | João Paulo dos Santos Benedito Leandro |
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Affiliation: | 1. Universidade de Brasília, Departamento de Matemática, 70910-900, Brasília-DF, Brazil;2. Universidade Federal de Jataí, CIEXA, BR 364, km 195, 3800, 75801-615, Jataí, GO, Brazil |
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Abstract: | We consider the static vacuum Einstein spacetime when the spatial factor is conformal to a n-dimensional pseudo-Euclidean space. The most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary differential equations is completely described. We obtain the entire set of solutions of the reduced system, where the classical Schwarzschild solution arises as a particular solution. In addition, we show that the Riemannian spatial factors associated to these solutions are foliated by parallel hypersurfaces of constant mean curvature. |
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Keywords: | Static spacetimes Exact solutions Reduction Conformal metrics Semi-Riemannian manifolds |
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