General Relativity from Einstein-Gauss-Bonnet gravity

TL;DR

This paper demonstrates how four-dimensional Einstein gravity can emerge from higher curvature Lovelock theories through a specific compactification process involving fluxes, leading to new black hole solutions and modified thermodynamics.

Contribution

It introduces a novel compactification method from higher-dimensional Lovelock theories to Einstein gravity without fine-tuning, including explicit examples and black hole solutions.

Findings

Einstein gravity derived from Lovelock theories via flux compactification.

Construction of black string and p-brane solutions with modified thermodynamics.

Discovery of entropy modifications affecting phase transitions and black hole dominance.

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 $p\geq1$. 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.