Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-08-18
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages, 24780 bytes
Scientific paper
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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