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A static Einstein metric that generalizes the Schwarzschild metric

José L. Martínez-Morales
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Abstract

A static Einstein metric that generalizes the Schwarzschild metric is considered. The event horizon is not necessarily a sphere and the term $dt\sp2$ is a function on such horizon. That the metric is Einstein establishes a relation between its terms. One demonstrates that the scalar curvature of the horizon is constant, and that the term $dt\sp2$ gives rise to (i) the metric of the horizon being Einstein, or (ii) the scalar curvature of the horizon being proportional to an eigenvalue of the Laplace operator.

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José L. Martínez-Morales. 2005-08-18. A static Einstein metric that generalizes the Schwarzschild metric. https://arxiv.org/abs/gr-qc/0508074

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