The black hole and FRW geometries of non-relativistic gravity

TL;DR

This paper explores non-relativistic Hořava-Lifshitz gravity, deriving black hole and cosmological solutions, demonstrating classical test compatibility, and constraining parameters via primordial helium abundance.

Contribution

It provides explicit black hole and cosmological solutions within Hořava-Lifshitz gravity and analyzes their physical properties and observational constraints.

Findings

Black hole solution analogous to Schwarzschild in HL gravity

Theory matches GR's Newtonian and post-Newtonian limits

Cosmological equations are identical to GR but constrained by helium abundance

Abstract

We consider the recently proposed non-relativistic Ho\v{r}ava-Lifshitz four-dimensional theory of gravity. We study a particular limit of the theory which admits flat Minkowski vacuum and we discuss thoroughly the quadratic fluctuations around it. We find that there are two propagating polarizations of the metric. We then explicitly construct a spherically symmetric, asymptotically flat, black hole solution that represents the analog of the Schwarzschild solution of GR. We show that this theory has the same Newtonian and post-Newtonian limits as GR and thus, it passes the classical tests. We also consider homogeneous and isotropic cosmological solutions and we show that although the equations are identical with GR cosmology, the couplings are constrained by the observed primordial abundance of ${}^4{\rm He}$.