Cosmic Strings in a Model of Non-relativistic Gravity

Hořava proposed a non-relativistic renormalizable theory of gravitation, which is reduced to general relativity (GR) in large distances (infra-red regime (IR)). It is believed that this theory is an ultra-violet (UV) completion for the classical theory of gravitation. In this paper, after a brief review of some fundamental features of this theory, we investigate it for a static cylindrical symmetric solution which describes Cosmic string as a special case. We have also investigated some possible solutions, and have seen that how the classical GR field equations are modified for generic potential V(g). In one case there is an algebraic constraint on the values of three coupling constants. Finally as a pioneering work we deduce the most general cosmic string in this theory. We explicitly show that how the coupling constants distort the mass parameter of cosmic string. We deduce an explicit function for mass per unit length of the space-time as a function of the coupling constants. We compare this function with another which Aryal et al. (Phys. Rev. D 34:2263, 1986) have found in GR. Also we calculate the self-force on a massive particle near Hořava-Lifshitz straight string and we give a typical order for the coupling constant g ₉. This order of magnitude proposes a cosmological test for validity of this theory.