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Dimensionally Continued Black Holes

Maximo Banados·Claudio Teitelboim·Jorge Zanelli
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Abstract

Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are studied. The action is, in odd dimensions, the Chern-Simons form for the anti-de Sitter group and, in even dimensions, the Euler density constructed with the Lorentz part of the anti-de Sitter curvature tensor. Both actions are special cases of the Lovelock action, and they reduce to the Hilbert action (with negative cosmological constant) in the lower dimensional cases $\mbox{$\cal D$}=3$ and $\mbox{$\cal D$}=4$. Exact black hole solutions characterized by mass ($M$) and electric charge ($Q$) are found. In odd dimensions a negative cosmological constant is necessary to obtain a black hole, while in even dimensions, both asymptotically flat and asymptotically anti-de Sitter black holes exist. The causal structure is analyzed and the Penrose diagrams are exhibited.

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Maximo Banados, Claudio Teitelboim, Jorge Zanelli. 1993-09-21. Dimensionally Continued Black Holes. https://doi.org/10.1103/physrevd.49.975

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