Analitical approximation of $<\phi^2>$ for a massive scalar field in static spherically symmetric spacetimes

TL;DR

This paper develops an analytical approximation for the vacuum expectation value of a massive scalar field squared in static spherically symmetric spacetimes, enabling calculations in Schwarzschild and wormhole geometries.

Contribution

It introduces a new analytical method for approximating $<\,\phi^2\,>$ in static spherically symmetric spacetimes, extending previous numerical approaches.

Findings

Approximation successfully applied to Schwarzschild spacetime.

Approximation also applied to wormhole spacetime.

Provides a practical tool for quantum field calculations in curved backgrounds.

Abstract

An analitical approximation of $<\phi^2>$ for a massive scalar field in a zero temperature vacuum state in static spherically symmetric spacetimes is obtained. The calculations are based on the method for computing vacuum expectations values for scalar fields in general static spherically symmetric spacetimes derived by Anderson, Hiscock and Samuel [Phys. Rev. D {\bf 51}, 4337 (1995)]. The analitical approximation is used to compute $<\phi^2>$ in Schwarzschild and wormhole spacetimes.