Exact black hole solutions in scalar-tensor theories

Abstract

General Relativity allows for a unique black hole solution, characterized by its mass M, angular momentum J, and electric charge Q. Black holes in General Relativity are thus said to have no hair, that is, no other independent physical quantity (no-hair theorem). Despite the numerous successes of General Relativity, some limitations remain, like the central singularity possessed by black holes, where the curvature of spacetime becomes infinite. Modified theories of gravity try to solve some of these shortcomings. This thesis tests the no-hair theorem in a popular modification of gravity, called scalar-tensor theories, where a unique degree of freedom (a scalar field) is added on top of the usual metric of spacetime of General Relativity. Using various symmetries, new black holes, called hairy black holes, are obtained. Some of them evade strongly the no-hair theorem, being characterized by a new quantity (primary scalar hair), distinct from M, J or Q. An interesting progress is also achieved, since in certain cases, the usual singularity disappears: the curvature of spacetime remains bounded even at the core of the black hole. Moreover, theoretical links are established between scalar-tensor theories (which take place in the usual four dimensions of spacetime), and theories of gravity in higher dimensions, by Kaluza-Klein reduction. Finally, certain particular properties of scalar-tensor theories enable to transform initial black hole solutions into other solutions with very distinct geometry, like wormholes or non-stationary black holes.