General Relativity from Einstein-Gauss-Bonnet gravity

Abstract

In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension $D=4+p$, being $p\ge 1$. The compactification is performed on a direct product space ${\mathcal{M}}_D={\mathcal{M}}_4\times {\mathcal{K}}^p$, where ${\mathcal{K}}^p$ is a Euclidean internal manifold of constant curvature. The process is carried out in such a way that no fine tuning between the coupling constants is needed. The compactification requires to dress the internal manifold with the flux of suitable $p$-forms whose field strengths are proportional to the volume form of the internal space. We explicitly compactify Einstein-Gauss-Bonnet theory from dimension six to Einstein theory in dimension four and sketch out a similar procedure for this compactification to take place starting from dimension five. Several black string/p-branes solutions are constructed, among which, a five dimensional asymptotically flat black string composed of a Schwarzschild black hole on the brane is particularly interesting. Finally, the thermodynamic of the solutions is described and we find that the consistent compactification modifies the entropy by including a constant term, which may induce a departure from the usual behavior of the Hawking-Page phase transition. New scenarios are possible in which large black holes dominate the canonical ensamble for all temperatures above the minimal value.

arXiv comment20 pages, 3 figures. v2: 20 pages, 2 figures, references added and typos fixed. To appear in Physical Review D

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• Holographic Anisotropic Background in 5D Einstien-Gauss-Bonnet Gravity
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