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Mining the geodesic equation for scattering data

Cheung, Clifford and Shah, Nabha and Solon, Mikhail P. (2021) Mining the geodesic equation for scattering data. Physical Review D, 103 (2). Art. No. 024030. ISSN 2470-0010. doi:10.1103/PhysRevD.103.024030.

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The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the presence of perturbatively small effects such as tidal distortion and higher derivative corrections to general relativity. We derive an algebraic map between the perturbed geodesic equation and the leading PM scattering amplitude at arbitrary mass ratio. As examples, we compute formulas for amplitudes and isotropic gauge Hamiltonians for certain infinite classes of tidal operators such as electric or magnetic Weyl to any power, and for higher derivative corrections to gravitationally interacting bodies with or without electric charge. Finally, we present a general method for calculating closed-form expressions for amplitudes and isotropic gauge Hamiltonians in the test-particle limit at all orders in the PM expansion.

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Additional Information:© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. Received 16 November 2020; accepted 18 December 2020; published 14 January 2021. We thank Andreas Helset and Jan Steinhoff for comments on the manuscript. We thank Zvi Bern, Julio Parra-Martinez, Radu Roiban, Eric Sawyer and Chia-Hsien Shen for helpful discussions, especially regarding their concurrent work [63]. C. C. and N. S. are supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics. M. P. S. is supported by the Mani L. Bhaumik Institute for Theoretical Physics and David Saxon Presidential Term Chair in Physics. We used Mathematica [77] in combination with xact [78].
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Mani L. Bhaumik Institute for Theoretical PhysicsUNSPECIFIED
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Issue or Number:2
Record Number:CaltechAUTHORS:20201111-130011003
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106618
Deposited By: Joy Painter
Deposited On:11 Nov 2020 22:28
Last Modified:16 Nov 2021 18:55

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