Four dimensional string solutions in Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper explores string-like solutions in four-dimensional Hořava-Lifshitz gravity, finding that certain Einstein gravity solutions are also valid, and identifying a unique BTZ black string solution for the IR limit.

Contribution

It demonstrates that Einstein gravity solutions, including BTZ black strings, are solutions in Hořava-Lifshitz gravity under specific conditions, and discovers a new uniform BTZ black string solution at the IR limit.

Findings

Einstein gravity solutions are also solutions in Hořava-Lifshitz gravity for vanishing Cotton tensor.

A new uniform BTZ black string solution exists at the IR limit (λ=1).

No solutions exist for λ ≠ 1.

Abstract

We investigate string-like solutions in four dimensions based on Ho\v{r}ava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black strings are solutions in Ho\v{r}ava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the "conformal" lapse function is not constrained in Ho\v{r}ava-Lifshitz gravity. It turns out that if $\lambda \ne 1$, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., $\lambda=1$), there exists an additional solution of which the conformal lapse function is determined. Interestingly, this solution admits a uniform BTZ black string along the string direction, which is distinguished from the warped BTZ black string in Einstein gravity. Therefore, it is a good candidate for the test of the theory.