Gravitational wave forms for extreme mass ratio collisions from supersymmetric gauge theories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929718499999744 |
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| author | Fucito, Francesco Morales, Jose Francisco Russo, Rodolfo |
| author_facet | Fucito, Francesco Morales, Jose Francisco Russo, Rodolfo |
| contents | We study the wave form emitted by a particle moving along an arbitrary (in general open) geodesic of the Schwarzschild geometry. The mathematical problem can be phrased in terms of quantities in ${\cal N}=2$ supersymmetric gauge theories that can be calculated by using localization and the AGT correspondence. In particular through this mapping, the post-Newtonian expansion of the wave form is expressed as a double instanton sum with rational coefficients that resums all tail contributions into Gamma functions and exponentials. The formulae we obtain are valid for generic values of the orbital quantum numbers $\ell$ and $m$. For $\ell=2,3$ we check explicitly that our results agree with the small mass ratio limit of the wave forms derived in the Multipole Post-Minkowskian and the amplitudes approaches. We show how the so-called tail and tail of tail contributions to the wave form arise in our approach. Finally, we derive a universal formula for the soft limit of the wave form that resums all logarithmic divergent terms of the form $ω^{n-1} (\log ω)^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gravitational wave forms for extreme mass ratio collisions from supersymmetric gauge theories Fucito, Francesco Morales, Jose Francisco Russo, Rodolfo High Energy Physics - Theory General Relativity and Quantum Cosmology We study the wave form emitted by a particle moving along an arbitrary (in general open) geodesic of the Schwarzschild geometry. The mathematical problem can be phrased in terms of quantities in ${\cal N}=2$ supersymmetric gauge theories that can be calculated by using localization and the AGT correspondence. In particular through this mapping, the post-Newtonian expansion of the wave form is expressed as a double instanton sum with rational coefficients that resums all tail contributions into Gamma functions and exponentials. The formulae we obtain are valid for generic values of the orbital quantum numbers $\ell$ and $m$. For $\ell=2,3$ we check explicitly that our results agree with the small mass ratio limit of the wave forms derived in the Multipole Post-Minkowskian and the amplitudes approaches. We show how the so-called tail and tail of tail contributions to the wave form arise in our approach. Finally, we derive a universal formula for the soft limit of the wave form that resums all logarithmic divergent terms of the form $ω^{n-1} (\log ω)^n$. |
| title | Gravitational wave forms for extreme mass ratio collisions from supersymmetric gauge theories |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2408.07329 |