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

Fuente: arXiv
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Main Authors: Zhang, Chao, Gong, Yungui, Lu, Xuchen, Zhou, Wenting
Format: Preprint
Published: 2026
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author Zhang, Chao
Gong, Yungui
Lu, Xuchen
Zhou, Wenting
author_facet Zhang, Chao
Gong, Yungui
Lu, Xuchen
Zhou, Wenting
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_27284
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The point-particle-limit effective-source approach for computing gravitational self-force in the Lorenz gauge
Zhang, Chao
Gong, Yungui
Lu, Xuchen
Zhou, Wenting
General Relativity and Quantum Cosmology
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.
title The point-particle-limit effective-source approach for computing gravitational self-force in the Lorenz gauge
topic General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2603.27284