Lovelock solutions in the presence of matter sources

Abstract

For a large class of space and time-dependent warped geometries we find the general solution of the six-dimensional Einstein-Gauss-Bonnet equations in the presence of $p$-form matter fields. This is done under two conditions on the matter sector which we show impose the integrability of the full system. Solutions are classified and known black hole limits are found. It is shown that Lovelock gravity restricts drastically the possible horizon geometries and allowed matter sources. In fact, we show that if we allow only for solutions of asymptotically flat falloff behavior, then the only permissible black hole is that of Boulware-Deser with electromagnetic charge. The situation of six-dimensional Lovelock gravity is therefore almost identical to four-dimensional General Relativity. The gravitational horizon constraints lead us to find static solutions involving 3-form matter fields in anti de Sitter space which are also new to General Relativity along with other cosmological and black string type of solutions.