Domain Wall solutions to Horava gravity

TL;DR

This paper explores gravitational domain wall solutions within Horava gravity, revealing two solution branches with distinct boundary behaviors depending on the cosmological constant, and analyzing their geometric properties.

Contribution

It presents new purely gravitational domain wall solutions in Horava gravity with detailed analysis of their structure and boundary conditions.

Findings

Existence of two solution branches for  > 1/3

Solutions with bounded space and singular boundaries for positive cosmological constant

Infinite extension with Lifshitz asymptotics for negative cosmological constant

Abstract

We investigated purely gravitational domain wall solutions to Horava nonrelativistic theory of gravity with detailed balance in 3 + 1 dimensions. We find that for arbitrary values of the running parameter {\lambda} > 1/3 two branches of membrane solutions exist. For positive values of the cosmo-logical constant, the solution represents a space that is bounded in the transverse direction, with singularities sitting at each of the boundaries. For negative values of the cosmological constant, the solution contains a single membrane sitting at the center of a space, which extends infinitely in the transverse direction approaching a Lifshitz metric. In that case there is one additional degenerate branch, for which the lapse function is undetermined.