Regularization of a scalar charged particle for generic orbits in Kerr spacetime

TL;DR

This paper advances the calculation of the self-force on a scalar charged particle in Kerr spacetime by deriving higher-order regularization parameters, enabling faster and more accurate modeling of particle motion relevant to gravitational wave research.

Contribution

It computes the next order of the Detweiler-Whiting singular field and regularization parameters for scalar particles in Kerr spacetime, improving computational efficiency.

Findings

Faster self-force calculations with fewer modes.

Enhanced regularization parameters for scalar fields.

Foundations for electromagnetic and gravitational extensions.

Abstract

A scalar charged particle moving in a curved background spacetime will emit a field affecting its own motion; the resolving of this resulting motion is often referred to as the self-force problem. This also serves as a toy model for the astrophysically interesting compact body binaries, extreme mass ratio inspirals, targets for the future space-based gravitational wave detector, LISA. In the modelling of such systems, a point-particle assumption leads to problematic singularities which need to be safely removed to solve for the motion of the particle regardless of the scenario: scalar, electromagnetic or gravitational. Here, we concentrate on a scalar charged particle and calculate the next order of the Detweiler-Whiting singular field and its resulting regularisation parameter when employing the mode-sum method of regularisation. This enables sufficiently faster self-force calculations giving the same level of accuracy with significantly less $\ell$ modes. Due to the similarity of the governing equations, this also lays the groundwork for similar calculations for an electromagnetic or mass charged particle in Kerr spacetime and has applications in other regularisation schemes like the effective source and matched expansion.