Four dimensional string solutions in Horava-Lifshitz gravity
Abstract
We investigate string-like solutions in four dimensions based on Horava-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 Horava-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 Horava-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. Therefore, it is a good candidate for the test of the theory.