Non static cosmic strings in Lyra geometry

TL;DR

This paper investigates the gravitational fields of non-static local and global cosmic strings within Lyra geometry, revealing that global strings exert an attractive gravitational force.

Contribution

It provides a novel analysis of cosmic strings in Lyra geometry, including exterior solutions and the gravitational nature of global strings, which was not previously explored.

Findings

Global strings have an attractive gravitational field.

Exterior solutions are independent of the radial distribution of the source.

Local string solutions use a Dirac delta approximation for energy density.

Abstract

The gravitational field of both local and global non static cosmic strings in the context of Lyra geometry are investigated. Local strings are characterized by having an energy momentum tensor whose only non null components are $T_{tt} = T_{zz}$ . As linearized Einstein equations are formally analogous to the Maxwell equations, the exterior solution does not depend on the radial distribution of the source and hence a Dirac d function was used to approximate the radial distribution of the energy momentum tensor for a local cosmic string along the z-axis: $T_{ab} = \delta(x) \delta(y)diag (\sigma, 0, 0, \sigma) $, $\sigma $being the energy density of the string [A.Vilenkin. Phys.Rep.(1985)121,263]. For a global string, the energy momentum tensor components are calculated from the action density for a complex scalar field y along with a Maxican hat potential. The gravitational field of the global string is shown to be attractive in nature.