Black holes and solitons in an extended Proca theory

Eugeny Babichev,Mokhtar Hassaine,Christos Charmousis

doi:10.1007/jhep05(2017)114

Abstract

We study a massive vector tensor theory that acquires mass via a standard Proca term but also via a higher order term containing an explicit coupling to curvature. We find static solutions that are asymptotically flat, adS or Lifshitz black holes. Since the higher order term regularizes the effect of the Proca mass term, generically solutions are asymptotically regular for arbitrary couplings. This is true in particular for asymptotically flat black holes. For a particular coupling we find particle like solitons that have a regular and non trivial geometry everywhere. In all adS solutions the Proca mass term plays the role of an effective cosmological constant distinctly different from the bare cosmological constant.

Highlights

JHEP05(2017)114 the micro-Gauss) as the magnetic field is strongly diluted during inflation; one has to go beyond Einstein Maxwell (EM) theory in order to pursue such and other effects, for example, related to the CMB [6]
Horndeski in a series of nice papers studied an extension of EM [11,12,13,14, 17, 18] for which he demonstrated that there is a unique additional term which can be added to EM enjoying the following properties: Maxwell equations in flat spacetime, U(1) gauge symmetry and second order field equations
The solutions we found are generically of adS asymptotics in the presence of a Proca mass term μ while they are asymptotically flat in the absence of μ but, generic β, see section 4

Summary

Theory and field equations

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]. R2, the metric constraint will imply that the effective cosmological constant is fixed in term of the Proca mass as μ2. The first one is obtained for a fixed coupling constant 1 = 4β, and in this case, we will be able to derive the general static solution with a maximal homogeneous 2 dimensional space. These solutions can be either black holes or solitons and both are asymptotically AdS.

The spherically symmetric adS black holes and solitons

Conclusions