Ground State Energy of Massive Scalar Field in the Background of Finite Thickness Cosmic String

TL;DR

This paper calculates the ground state energy of a massive scalar field around a finite-thickness cosmic string, revealing how it varies with string radius and coupling parameters using zeta regularization.

Contribution

It provides a detailed calculation of the ground state energy in the Gott-Hiscock metric, including renormalization and heat kernel coefficients, in a finite-thickness cosmic string background.

Findings

Finite part of energy vanishes with increasing string radius.

Energy depends on the nonconformal coupling parameter ξ.

Numerical analysis confirms the energy's behavior in 2+1 dimensions.

Abstract

We calculate the ground state energy of a massive scalar field in the background of a cosmic string of finite thickness (Gott-Hiscock metric). Using zeta functional regularization we discuss the renormalization and the relevant heat kernel coefficients in detail. The finite (non local) part of the ground state energy is calculated in 2+1 dimensions in the approximation of a small mass density of the string. By a numerical calculation it is shown to vanish as a function of the radius of the string and of the parameter $\xi$ of the nonconformal coupling.