Cosmic strings in a model of non-relativistic gravity

Abstract

Ho$\check{\text{r}}$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$\check{\text{r}}$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.

30pages,It has been accepted for publication in International Journal of Theoretical Physics-Extended version with 2 new sections about (Thermodynamics and Dark energy in Horava-Lifshitz gravity),(About the existence of non-static cylindrical solutions)

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• Observational constraints on non-minimally coupled Galileon model
• Planar Symmetry in f(T) gravity
• Noether Gauge Symmetry of Modified Teleparallel Gravity Minimally Coupled with a Canonical Scalar Field
• Cylindrical solutions in Mimetic gravity
• A Slowly Rotating Black Hole in Horava-Lifshitz Gravity and a 3+1 Dimensional Topological Black Hole: Motion of Particles and BSW Mechanism
• Cosmic string in gravity's rainbow
• Killing and Noether Symmetries of Plane Symmetric Spacetime
• Thermodynamics and geometry of strange quark matter
• Inflation driven by q-de Sitter
• Exploring Self-Gravitating Cylindrical Structures in Modified Gravity: Insights from Scalar-Vector-Tensor Theory