Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime
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arXiv
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| Format: | Preprint |
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2025
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| author | Zhang, Chao Cai, Rong-gen Fu, Guoyang Gong, Yungui Lu, Xuchen Zhou, Wenting |
| author_facet | Zhang, Chao Cai, Rong-gen Fu, Guoyang Gong, Yungui Lu, Xuchen Zhou, Wenting |
| contents | The numerical calculation of gravitational self-force in extreme mass ratio inspiral systems is fundamentally challenging due to the singular nature of point-particle sources. To overcome these difficulties, the effective source method offers an innovative alternative by replacing traditional regularization techniques with a reformulation of the problem. In this paper, we present the first fully analytic framework for constructing effective sources to compute the gravitational self-force for generic orbits in Schwarzschild spacetime. By reformulating the singular field through angular modulation in terms of a tetrad decomposition, the effective source can be constructed with the linear combination of scalar modes. The derived effective source is continuous across the particle's worldline, enabling efficient numerical implementation in $1+1$ dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime Zhang, Chao Cai, Rong-gen Fu, Guoyang Gong, Yungui Lu, Xuchen Zhou, Wenting General Relativity and Quantum Cosmology The numerical calculation of gravitational self-force in extreme mass ratio inspiral systems is fundamentally challenging due to the singular nature of point-particle sources. To overcome these difficulties, the effective source method offers an innovative alternative by replacing traditional regularization techniques with a reformulation of the problem. In this paper, we present the first fully analytic framework for constructing effective sources to compute the gravitational self-force for generic orbits in Schwarzschild spacetime. By reformulating the singular field through angular modulation in terms of a tetrad decomposition, the effective source can be constructed with the linear combination of scalar modes. The derived effective source is continuous across the particle's worldline, enabling efficient numerical implementation in $1+1$ dimensions. |
| title | Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.19732 |