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

Understand

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.