Spherically symmetric solutions in modified Horava-Lifshitz gravity

TL;DR

This paper derives spherically symmetric solutions in a modified version of Hořava-Lifshitz gravity, analyzing their properties and how they alter Newtonian gravity at large distances, especially with a non-zero cosmological constant.

Contribution

It provides new spherically symmetric solutions in a recently proposed modified Hořava-Lifshitz gravity, including analysis of their behavior and constraints on coupling constants.

Findings

Solutions similar to four-derivative action cases

Constraints on new coupling constants derived

Newton's law modified at large distances with cosmological constant

Abstract

We find spherically symmetric solutions in the modified Ho\v{r}ava-Lifshitz gravity proposed recently by Blas, Pujolas and Sibiryakov. The non-linear equations of the two derivative action turn out to be similar to those stemming from the four-derivative action explored recently. We analyze the solutions and derive constraints on the relevant new coupling constant. We also analyze the case where the cosmological constant is non-zero. We derive the large distance expansion of solutions and show that the power of the standard Newton's law is modified in the presence of a cosmological constant.