Black holes and Abelian symmetry breaking

Abstract

Black hole configurations offer insights on the non-linear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector-tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector-tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarization, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.

Black holes and solitons in an extended Proca theory

“…These behaviors are in agreement with the asymptotically flat solutions or conical geometries (for Λ = 0) found in [41]. In the next two sections, we will report on two generic classes of solutions.…”

“…It is known that Einstein-Proca theories for example do not admit hairy solutions as was discussed by Bekenstein, [38][39][40]. We will see that the additional curvature-vector term modifies this conclusion providing hairy black holes (see also [41,42]) for asymptotically flat spacetimes. Putting these considerations together we will consider the following action…”

“…An interesting twist of this solution happens for β = 1/4 and the same spacetime (Schwarzschild) metric. Here, because the right hand side of (2.8) drops out, allows us to have a non-trivial electric field a(r) = q + Q/r which is the interesting asymptotically flat solution found in [41]. If we allow for µ = 0 we can get get counterpart solutions to the self tuning de Sitter black holes of [36] found in [43].…”

“…Recently there was some activity finding hairy solutions for the above theory [41,43,44]. For the case µ = 0 the case of a particular coupling β = 1/4 was studied [41].…”

“…For the case µ = 0 the case of a particular coupling β = 1/4 was studied [41]. There it was postulated that only for this particular coupling there existed asymptotically flat solutions.…”