Lovelock-Lifshitz black holes

Abstract

In this paper, we investigate the existence of Lifshitz solutions in Lovelock gravity, both in vacuum and in the presence of a massive vector field. We show that the Lovelock terms can support the Lifshitz solution provided the constants of the theory are suitably chosen. We obtain an exact black hole solution with Lifshitz asymptotics of any scaling parameter z in both Gauss-Bonnet and in pure 3rd order Lovelock gravity. If matter is added in the form of a massive vector field, we also show that Lifshitz solutions in Lovelock gravity exist; these can be regarded as corrections to Einstein gravity coupled to this form of matter. For this form of matter we numerically obtain a broad range of charged black hole solutions with Lifshitz asymptotics, for either sign of the cosmological constant. We find that these asymptotic Lifshitz solutions are more sensitive to corrections induced by Lovelock gravity than are their asymptotic AdS counterparts. We also consider the thermodynamics of the black hole solutions and show that the temperature of large black holes with curved horizons is proportional to r z 0 where z is the critical exponent; this relationship holds for black branes of any size. As is the case for asymptotic AdS black holes, we find that an extreme black hole exists only for the case of horizons with negative curvature. We also find that these Lovelock-Lifshitz black holes have no unstable phase, in contrast to the Lovelock-AdS case. We also present a class of rotating Lovelock-Lifshitz black holes with Ricci-flat horizons.

Lifshitz black holes in IIA supergravity

“…By engineering a matter or gravity content to source the desired geometry, some analytical solutions have also been constructed. Overall, Lifshitz black hole solutions in phenomenological models include numerical and analytic studies, fixed as well as arbitrary critical exponents, horizons with various topologies, extensions to other dimensions, higher-order theories of gravity, and Brans-Dicke models [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”

“…Analytic LiBH solutions have been found for essentially two types of 4D Einstein gravity systems (see also [37][38][39][40][41][42][43][44] for other possible extensions). The first (ΛAAm) contains, besides gravity, a cosmological constant, a massless abelian gauge field F 2 and massive abelian gauge field F 2 with mass m [26].…”

Asymptotically Lifshitz wormholes and black holes for Lovelock gravity in vacuum

“…A concrete example in this vein was first provided by the so-called Lifshitz spacetimes in Ref. [20] (see also [21]), and thereafter a wide class of asymptotically Lifshitz solutions have been found, either analytic [15,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] or numerical [38][39][40][41][42][43][44].…”

Quasitopological Reissner-Nordström black holes

“…It would be interesting to see the modifications to these behaviours in a Lifshitz symmetric gravitational theory [31,32] with higher order quasi-topological terms. Another interesting phenomenon is the surprising result of instability of RN black holes in dimensions greater than 6 [33].…”