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Title: From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

Abstract

We recently introduced in [9] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following — remarkably simple — formula relating the periastron advance to the scattering angle: $ΔΦ(J,ε)=χ(J,ε)+χ(-J,ε)$, via analytic continuation in angular momentum and binding energy. Using explicit expressions from [9], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [9] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angularmore » momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized ‘impetus formula’ for spinning bodies and black holes as ‘elementary particles’. Our findings here and in [9] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.« less

Authors:
 [1];  [2]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States); Uppsala Univ. (Sweden)
  2. Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1608799
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Kälin, Gregor, and Porto, Rafael A. From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist). United States: N. p., 2020. Web. https://doi.org/10.1007/jhep02(2020)120.
Kälin, Gregor, & Porto, Rafael A. From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist). United States. https://doi.org/10.1007/jhep02(2020)120
Kälin, Gregor, and Porto, Rafael A. Thu . "From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)". United States. https://doi.org/10.1007/jhep02(2020)120. https://www.osti.gov/servlets/purl/1608799.
@article{osti_1608799,
title = {From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)},
author = {Kälin, Gregor and Porto, Rafael A.},
abstractNote = {We recently introduced in [9] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following — remarkably simple — formula relating the periastron advance to the scattering angle: $ΔΦ(J,ε)=χ(J,ε)+χ(-J,ε)$, via analytic continuation in angular momentum and binding energy. Using explicit expressions from [9], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [9] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized ‘impetus formula’ for spinning bodies and black holes as ‘elementary particles’. Our findings here and in [9] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.},
doi = {10.1007/jhep02(2020)120},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2020,
place = {United States},
year = {2020},
month = {2}
}

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Works referenced in this record:

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