Asymptotically Lifshitz wormholes and black holes for Lovelock gravity in vacuum

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 1 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(z(2) 1) + 1 = l(2)/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)pi l. 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.