Asymptotically Lifshitz wormholes and black holes for Lovelock gravity in vacuum

TL;DR

This paper constructs and analyzes vacuum Lifshitz wormholes and black holes in higher-dimensional Lovelock gravity, revealing their geometric properties, causal structure, and thermodynamics, and introduces new solutions with diverse boundary geometries.

Contribution

It presents the first explicit vacuum Lifshitz wormhole and black hole solutions in higher-dimensional Lovelock gravity with detailed geometric and thermodynamic analysis.

Findings

Existence of regular Lifshitz wormholes connecting two asymptotic Lifshitz spacetimes.

Black holes with fixed Hawking temperature related to the dynamical exponent z.

New analytic solutions including pure Lifshitz spacetimes and interpolating wormholes.

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(z^2-1)+1=(l/L)^2, where L 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.