Black Holes in Einstein - Lovelock Gravity ∗

Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are found. In even dimensions the solution has many similarities with the Schwarzschild metric. In odd dimensions, the equations of motion are explicitly anti de-Sitter invariant, and the solution is alike in many ways to the 2+1 black hole. This talk will be devoted to the study of lower and higher dimensional black holes in the Einstein-Lovelock theory of gravity . The results presented here have been developed in collaboration with C. Teitelboim and J. Zanelli [1,2]. I thank them for their great encouragment and guidance while this work was in preparation. Of course, errors and omitions in this report are my responsability. In dimensions greater than four the usual Einstein equations are not the most general equations that give rise to second order tensorial equations for the metric. In contrast, a large class of equations, parametrized by a number of independent dimensionful parameters, can be considered [3]. This equations are known as Einstein-Lovelock equations. In this work black-hole solutions for a particular class of these equations will be found. ∗Talk given at the VIII Latin American Symposium on Relativity and Gravitation, SILARG, Sao Paulo, July 1993.