Renormalization for self-potential of a scalar charge in static space-times

TL;DR

This paper introduces a renormalization method for the self-potential of a static scalar charge in curved space-times, applicable to arbitrary mass and curvature coupling, and analyzes the self-force in the short Compton wavelength limit.

Contribution

The paper develops a new renormalization technique for scalar self-potential in static curved space-times, accommodating arbitrary mass and curvature coupling.

Findings

Derived the asymptotic behavior of self-potential for small Compton wavelength.

Calculated the self-force in the limit of small Compton wavelength.

Provided a general method applicable to various scalar field parameters.

Abstract

A method is presented which allows for the renormalization of the self-potential for a scalar point charge at rest in static curved space-time. The method is suitable for the scalar field with arbitrary mass $m$ and coupling to the scalar curvature. The asymptotic behavior of self-potential is obtained in the limit in which the Compton wave-length $1/m$ of the massive scalar field is much smaller than the characteristic scale of curvature of the background gravitational field. The self-force is calculated in this limit.