Four dimensional string solutions in Hořava-Lifshitz gravity

We investigate string-like solutions in four dimensions based on Hořava-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 Hořava-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 Hořava-Lifshitz gravity. It turns out that if λ ≠ 1, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., λ = 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. We also point out that this solution is exactly the same with the black string solution obtained in a low-energy string theory action including the dilaton and the Kalb-Ramond fields.