The point-particle-limit effective-source approach for computing gravitational self-force in the Lorenz gauge
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918414567604224 |
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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 |
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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 |