Charged Throats in the Ho\v{r}ava--Lifshitz Theory

TL;DR

This paper derives and analyzes a charged, spherically symmetric solution in Hořava–Lifshitz gravity, revealing conditions for a charged throat that connects Minkowski space to a singular manifold, and recovering known solutions in specific limits.

Contribution

It presents the first explicit charged throat solution in Hořava–Lifshitz gravity, extending the understanding of non-relativistic quantum gravity models with gauge interactions.

Findings

Solution reduces to Reissner–Nordström in the relativistic limit.

Existence of a charged throat depends on a specific mass-charge relation.

External solution approaches Reissner–Nordström spacetime when coupling constants tend to relativistic values.

Abstract

A spherically symmetric solution of the field equations of the Ho\v{r}ava--Lifshitz gravity--gauge vector interaction theory is obtained and analyzed. It describes a charged throat. The solution exists provided a restriction on the relation between the mass and charge is satisfied. The restriction reduces to the Reissner--Nordstr\"{o}m one in the limit in which the coupling constants tend to the relativistic values of General Relativity. We introduce the correct charts to describe the solution across the entire manifold, including the throat connecting an asymptotic Minkowski space--time with a singular 3+1 dimensional manifold. The solution external to the throat on the asymptotically flat side tends to the Reissner--Nordstr\"{o}m space--time at the limit when the coupling parameter, associated with the term in the low energy Hamiltonian that manifestly breaks the relativistic symmetry, tends to zero. Also, when the electric charge is taken to be zero the solution becomes the spherically symmetric and static solution of the Ho\v{r}ava--Lifshitz gravity.