Cosmic strings in a model of non-relativistic gravity

TL;DR

This paper explores cosmic string solutions within Hořava's non-relativistic gravity, revealing how coupling constants influence string properties and proposing potential cosmological tests for the theory's validity.

Contribution

It derives the most general cosmic string solutions in Hořava gravity and analyzes how coupling constants modify their characteristics compared to general relativity.

Findings

Coupling constants distort the mass parameter of cosmic strings.

Explicit function for mass per unit length as a function of coupling constants.

Order of magnitude estimate for coupling constants suggests possible cosmological tests.

Abstract

Ho$\check{\textbf{r}}$ava 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 \emph{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 \emph{cosmic string} in this theory. We explicitly show that how the \emph{coupling constants} distort the mass parameter of \emph{cosmic string}. We deduce an explicit function for mass per unit length of the space-time as a function of the \emph{coupling constants}. We compare this function with another which Aryal et al [58] have found in GR.Also we calculate the self-force on a massive particle near Ho$\check{\textbf{r}}$ava-Lifshitz straight string and we give a typical order for the \emph{coupling constants} $g_{9}$. This order of magnitude proposes a cosmological test for validity of this theory.