Wormholes in Horava gravity with cosmological constant

TL;DR

This paper explores static, spherically symmetric solutions in Horava gravity with a negative cosmological constant, revealing wormhole geometries with deformed AdS asymptotics and singular solutions, using analytical and numerical methods.

Contribution

It identifies and characterizes wormhole and singular solutions in Horava gravity with a negative cosmological constant, including their asymptotic behaviors and deviations from general relativity.

Findings

Existence of wormhole solutions with two sides joined by a throat.

Presence of solutions with naked singularities at the origin.

Asymptotic deformation of AdS and Lifshitz scaling in wormhole geometries.

Abstract

By combining analytical and numerical methods we find that the solutions of the complete Horava theory with negative cosmological constant that satisfy the conditions of staticity, spherical symmetry and vanishing of the shift function are two kinds of geometry: (i) a wormhole-like solution with two sides joined by a throat and (ii) a single side with a naked singularity at the origin. We study the second-order effective action. We consider the case when the coupling constant of the (partial ln N)^2 term, which is the unique deviation from general relativity in the effective action, is small. At one side the wormhole acquires a kind of deformed AdS asymptotia and at the other side there is an asymptotic essential singularity. The deformation of AdS essentially means that the lapse function N diverges asymptotically a bit faster than AdS. This can also be interpreted as an anisotropic Lifshitz scaling that the solutions acquire asymptotically.