Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond
Abstract We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for N non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for N > 2 are described including the subtraction of tree-like iteration contribu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2023)105 |
| _version_ | 1827900104458108928 |
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| author | Callum R. T. Jones Mikhail Solon |
| author_facet | Callum R. T. Jones Mikhail Solon |
| author_sort | Callum R. T. Jones |
| collection | DOAJ |
| description | Abstract We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for N non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for N > 2 are described including the subtraction of tree-like iteration contributions and the calculation of non-trivial many-body Fourier transform integrals needed to construct position space potentials. A new approach to calculating these integrals as an expansion in the hierarchical limit is described based on the method of regions. As an explicit example, we present the O $$ \mathcal{O} $$ (G 2) 3-body momentum space potential in general relativity as well as for charged bodies in Einstein-Maxwell. The result is shown to be in perfect agreement with previous post-Newtonian calculations in general relativity up to O $$ \mathcal{O} $$ (G 2 v 4). Furthermore, in appropriate limits the result is shown to agree perfectly with relativistic probe scattering in multi-center extremal black hole backgrounds and with the scattering of slowly-moving extremal black holes in the moduli space approximation. |
| first_indexed | 2024-03-12T23:26:30Z |
| format | Article |
| id | doaj.art-bf8e9e0e630844118c04604d8377b4c2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T23:26:30Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-bf8e9e0e630844118c04604d8377b4c22023-07-16T11:07:21ZengSpringerOpenJournal of High Energy Physics1029-84792023-02-012023214310.1007/JHEP02(2023)105Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyondCallum R. T. Jones0Mikhail Solon1Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California Los AngelesMani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California Los AngelesAbstract We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for N non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for N > 2 are described including the subtraction of tree-like iteration contributions and the calculation of non-trivial many-body Fourier transform integrals needed to construct position space potentials. A new approach to calculating these integrals as an expansion in the hierarchical limit is described based on the method of regions. As an explicit example, we present the O $$ \mathcal{O} $$ (G 2) 3-body momentum space potential in general relativity as well as for charged bodies in Einstein-Maxwell. The result is shown to be in perfect agreement with previous post-Newtonian calculations in general relativity up to O $$ \mathcal{O} $$ (G 2 v 4). Furthermore, in appropriate limits the result is shown to agree perfectly with relativistic probe scattering in multi-center extremal black hole backgrounds and with the scattering of slowly-moving extremal black holes in the moduli space approximation.https://doi.org/10.1007/JHEP02(2023)105Black HolesClassical Theories of GravityEffective Field TheoriesScattering Amplitudes |
| spellingShingle | Callum R. T. Jones Mikhail Solon Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond Journal of High Energy Physics Black Holes Classical Theories of Gravity Effective Field Theories Scattering Amplitudes |
| title | Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond |
| title_full | Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond |
| title_fullStr | Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond |
| title_full_unstemmed | Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond |
| title_short | Scattering amplitudes and N-body post-Minkowskian Hamiltonians in general relativity and beyond |
| title_sort | scattering amplitudes and n body post minkowskian hamiltonians in general relativity and beyond |
| topic | Black Holes Classical Theories of Gravity Effective Field Theories Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP02(2023)105 |
| work_keys_str_mv | AT callumrtjones scatteringamplitudesandnbodypostminkowskianhamiltoniansingeneralrelativityandbeyond AT mikhailsolon scatteringamplitudesandnbodypostminkowskianhamiltoniansingeneralrelativityandbeyond |