General relativity from Einstein-Gauss-Bonnet gravity

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 dimension $D=4+p$, being $p\geq1$. The is performed on direct product space $\mathcal{M}_D=\mathcal{M}_4\times\mathcal{K}^p$, where $\mathcal{K}^p$ Euclidean internal manifold constant curvature. process carried out such way no fine tuning between coupling constants needed. requires to dress with flux suitable $p$-forms whose field strengths are proportional volume form space. We explicitly compactify Einstein-Gauss-Bonnet six and sketch similar procedure for take place starting five. Several black string/p-branes solutions constructed, among which, five dimensional asymptotically flat string composed Schwarzschild hole brane particularly interesting. Finally, thermodynamic described find consistent modifies entropy by including term, which may induce departure usual behavior Hawking-Page phase transition. New scenarios possible large holes dominate canonical ensamble all temperatures above minimal value.