The point-particle-limit effective-source approach for computing gravitational self-force in the Lorenz gauge

TL;DR

This paper introduces a new effective-source method that simplifies the calculation of gravitational self-force by analytically taking the source size to zero, improving accuracy and efficiency.

Contribution

The paper presents the point-particle-limit effective source method, enabling more precise and computationally efficient self-force calculations in gravitational physics.

Findings

The new method accurately computes gravitational self-force in the Lorenz gauge.

Comparison shows the point-particle-limit method outperforms traditional approaches.

The approach provides a foundation for simulating generic geodesic orbits.

Abstract

The traditional effective-source method is hampered by complex analytical expressions and the inherent smoothness limit, which incur high computational costs and complicate implementation. To overcome these limitations, we introduce the point-particle-limit effective source method, which analytically takes the size of the effective source to zero, thereby transforming the problem into a well-defined jump condition of retarded metric field at the particle position governed by the local singular field. This formulation naturally pairs with a discontinuous Galerkin scheme, whose inherent capacity for accommodating solution discontinuities enables highly accurate enforcement of the jump conditions. We apply both the traditional and point-particle-limit effective source method to calculate the time-domain gravitational metric perturbation and gravitational self-force in the Lorenz gauge on a point particle in a circular orbit around a Schwarzschild black hole. The comparison of numerical results shows the excellent advantage of the point-particle-limit effective source method, which validates the correctness and efficiency of the point-particle-limit effective source method and thereby establishes a numerical foundation for computing generic geodesic orbits or long-time self-consistent orbital evolution.