Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911196260597760 |
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| author | Long, Oliver Whittall, Christopher Barack, Leor |
| author_facet | Long, Oliver Whittall, Christopher Barack, Leor |
| contents | Geodesic scattering of a test particle off a Schwarzschild black hole can be parameterized by the speed-at-infinity $v$ and the impact parameter $b$, with a "separatrix", $b=b_c(v)$, marking the threshold between scattering and plunge. Near the separatrix, the scattering angle diverges as $\sim\log(b-b_c)$. The self-force correction to the scattering angle (at fixed $v,b$) diverges even faster, like $\sim A_1(v)b_c/(b-b_c)$. Here we numerically calculate the divergence coefficient $A_1(v)$ in a scalar-charge toy model. We then use our knowledge of $A_1(v)$ to inform a resummation of the post-Minkowskian expansion for the scattering angle, and demonstrate that the resummed series agrees remarkably well with numerical self-force results even in the strong-field regime. We propose that a similar resummation technique, applied to a mass particle subject to a gravitational self-force, can significantly enhance the utility and regime of validity of post-Minkowskian calculations for black-hole scattering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory Long, Oliver Whittall, Christopher Barack, Leor General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory Geodesic scattering of a test particle off a Schwarzschild black hole can be parameterized by the speed-at-infinity $v$ and the impact parameter $b$, with a "separatrix", $b=b_c(v)$, marking the threshold between scattering and plunge. Near the separatrix, the scattering angle diverges as $\sim\log(b-b_c)$. The self-force correction to the scattering angle (at fixed $v,b$) diverges even faster, like $\sim A_1(v)b_c/(b-b_c)$. Here we numerically calculate the divergence coefficient $A_1(v)$ in a scalar-charge toy model. We then use our knowledge of $A_1(v)$ to inform a resummation of the post-Minkowskian expansion for the scattering angle, and demonstrate that the resummed series agrees remarkably well with numerical self-force results even in the strong-field regime. We propose that a similar resummation technique, applied to a mass particle subject to a gravitational self-force, can significantly enhance the utility and regime of validity of post-Minkowskian calculations for black-hole scattering. |
| title | Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.08363 |