Four dimensional string solutions in Hov{r}ava-Lifshitz gravity

We investigate string-like solutions in four dimensions based on Hov{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 Hov{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 Hov{r}ava-Lifshitz gravity. It turns out that if $lambda e 1$, 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.

Spacetime structure of 5D hypercylindrical vacuum solutions with tension

We investigate geometrical properties of 5D cylindrical vacuum solutions with a transverse spherical symmetry. The metric is uniform along the fifth direction and characterized by tension and mass densities. The solutions are classified by the tension-to-mass ratio. One particular example is the well-known Schwarzschild black string which has a curvature singularity enclosed by a horizon. We focus mainly on geometry of other solutions which possess a naked singularity. The light signal emitted by an object approaching the singularity reaches a distant observer with finite time, but is infinitely red-shifted.