Lovelock solutions in the presence of matter sources

TL;DR

This paper derives the general solutions for 6D Einstein-Gauss-Bonnet gravity with matter, classifies black hole solutions, and finds new static and cosmological solutions under specific conditions.

Contribution

It provides the first comprehensive classification of Lovelock gravity solutions with matter in six dimensions, revealing restrictions on horizon geometries and matter sources.

Findings

Only Boulware-Deser black holes with electromagnetic charge are allowed under certain conditions.

New static solutions with 3-form fields in anti-de Sitter space are discovered.

The horizon constraints lead to novel cosmological and black string solutions.

Abstract

For a large class of space and time-dependent warped geometries we find the general solution of the 6-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 behaviour, and no fine-tuning of coupling constants, then the only permissible black hole is that of Boulware-Deser with electromagnetic charge. The situation of 6 dimensional Lovelock gravity is therefore almost identical to 4 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.