Spherical Symmetric Solutions in Ho\v{r}ava-Lifshitz Gravity and their Properties

TL;DR

This paper explores the diverse set of spherically symmetric solutions in non-projectable Hořava-Lifshitz gravity with λ=1, analyzing their properties and the implications of their invariance under certain transformations.

Contribution

It identifies an infinite family of solutions parametrized by a function g^2(r) and examines their physical significance and behavior within the theory.

Findings

Solutions form an infinite set parametrized by g^2(r)

In IR limit, solutions relate to GR invariance under reparametrization

Symmetry is broken by matter terms in the action

Abstract

Non-projectable Ho\v{r}ava gravity for a spherically symmetric configuration with $\lambda=1$ exhibits an infinite set of solutions parametrized by a generic function $g^{2}(r)$ for the radial component of the shift vector. In the IR limit the infinite set of solutions corresponds to the invariance of General Relativity under a spacetime reparametrization. In general, not being a coordinate transformation, the symmetry in the action responsible for the infinite set of solutions does not have a clear physical interpretation. Indeed it is broken by the matter term in the action. We study the behavior of the solutions for generic values of the parameter $g^{2}(r)$.