From boundary data to bound states
Abstract We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections be...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)072 |
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| author | Gregor Kälin Rafael A. Porto |
| author_facet | Gregor Kälin Rafael A. Porto |
| author_sort | Gregor Kälin |
| collection | DOAJ |
| description | Abstract We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the twobody problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance ∆Φ) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bernet al. [36, 37], we readily derive Ω(E) and ∆Φ(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy. |
| format | Article |
| id | doaj-art-7d86faa799b0455bbdf9dc9048f5279a |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-7d86faa799b0455bbdf9dc9048f5279a2025-02-09T12:06:26ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020114910.1007/JHEP01(2020)072From boundary data to bound statesGregor Kälin0Rafael A. Porto1Department of Physics and Astronomy, Uppsala UniversityDeutsches Elektronen-Synchrotron DESYAbstract We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the twobody problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance ∆Φ) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bernet al. [36, 37], we readily derive Ω(E) and ∆Φ(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.https://doi.org/10.1007/JHEP01(2020)072Classical Theories of GravityScattering Amplitudes |
| spellingShingle | Gregor Kälin Rafael A. Porto From boundary data to bound states Journal of High Energy Physics Classical Theories of Gravity Scattering Amplitudes |
| title | From boundary data to bound states |
| title_full | From boundary data to bound states |
| title_fullStr | From boundary data to bound states |
| title_full_unstemmed | From boundary data to bound states |
| title_short | From boundary data to bound states |
| title_sort | from boundary data to bound states |
| topic | Classical Theories of Gravity Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP01(2020)072 |
| work_keys_str_mv | AT gregorkalin fromboundarydatatoboundstates AT rafaelaporto fromboundarydatatoboundstates |