Asymptotically Lifshitz wormholes and black holes for Lovelock gravity in vacuum

Abstract

Static asymptotically Lifshitz wormholes and black holes in vacuum are shown to exist for a class of Lovelock theories in d = 2n + 1 > 7 dimensions, selected by requiring that all but one of their n maximally symmetric vacua are AdS of radius l and degenerate. The wormhole geometry is regular everywhere and connects two Lifshitz spacetimes with a nontrivial geometry at the boundary. The dynamical exponent z is determined by the quotient of the curvature radii of the maximally symmetric vacua according to n(L 2 , where L 2 corresponds to the curvature radius of the nondegenerate vacuum. Light signals are able to connect both asymptotic regions in finite time, and the gravitational field pulls towards a fixed surface located at some arbitrary proper distance to the neck. The asymptotically Lifshitz black hole possesses the same dynamical exponent and a fixed Hawking temperature given by T = z 2 z πl . Further analytic solutions, including pure Lifshitz spacetimes with a nontrivial geometry at the spacelike boundary, and wormholes that interpolate between asymptotically Lifshitz spacetimes with different dynamical exponents are also found.

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].…”

Phase transitions for Lifshitz black holes

“…Analytic black hole solution with z = 2 that asymptotes planar Lifshitz spacetimes was found in the Einsteinscalar-massive vector theory [12] and in the Einstein-scalar-Maxwell theory [13]. Another analytic solution has been recently found in the Lovelock gravity [14]. The z = 3 Lifshitz black hole [15] was derived from the new massive gravity (NMG) in three-dimensional spacetimes [16].…”

Nonlinearly charged Lifshitz black holes for any exponent z > 1

“…We are also convinced that nonlinear electrodynamics will still be useful to explore Lifshitz black hole solutions and its generalizations in contexts beyond standard gravity, as for example for the Lovelock gravity [17] or even in higher-order gravity theories [15,16,18,19].…”

“…From the very beginning of the Lifshitz advent it becomes clear that pure Einstein gravity with eventually a cosmological constant resists to support such configurations, since it is clear from Birkhoff's theorem and its generalizations that in highly symmetric vacuum situations there is no freedom to choose the boundary conditions and they become fixed by the dynamics. Consequently, Lifshitz asymptotic requires the introduction of matter sources [5][6][7][8][9][10][11][12][13][14] or/and to consider higher-curvature gravity theories [15][16][17][18][19]. One of the first and simplest examples that has been used for supporting the Lifshitz spacetimes at any dimension D is a Proca field coupled to Einstein gravity with a negative cosmological constant [5].…”