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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. doi: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:

Observables and amplitudes for spinning particles and black holes
journal, December 2019

  • Maybee, Ben; O’Connell, Donal; Vines, Justin
  • Journal of High Energy Physics, Vol. 2019, Issue 12
  • DOI: 10.1007/JHEP12(2019)156

Classical space–times from the S-matrix
journal, December 2013


General relativistic dynamics of compact binaries at the third post-Newtonian order
journal, February 2001


Higher-order relativistic periastron advances and binary pulsars
journal, February 1988


Aligned spins: orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders
journal, December 2012


Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. II. Renormalized Lagrangian
journal, July 2019


Next to leading order spin(1)spin(1) effects in the motion of inspiralling compact binaries
journal, August 2008


From Boundary Data to Bound States
text, January 2019

  • Kälin, Gregor; Porto Pereira, Rafael Alejandro
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2020-00198

Next-to-leading-order spin–orbit effects in the motion of inspiralling compact binaries
journal, August 2010


Spin(1)spin(2) effects in the motion of inspiralling compact binaries at third order in the post-Newtonian expansion
journal, August 2008


Kerr black holes as elementary particles
journal, January 2020

  • Arkani-Hamed, Nima; Huang, Yu-tin; O’Connell, Donal
  • Journal of High Energy Physics, Vol. 2020, Issue 1
  • DOI: 10.1007/JHEP01(2020)046

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
journal, December 2018


Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
journal, May 2019


Black hole binary dynamics from the double copy and effective theory
journal, October 2019

  • Bern, Zvi; Cheung, Clifford; Roiban, Radu
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/JHEP10(2019)206

Lamb shift and the gravitational binding energy for binary black holes
journal, July 2017


Apparent ambiguities in the post-Newtonian expansion for binary systems
journal, July 2017


Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
journal, July 2000


First law of mechanics for compact binaries on eccentric orbits
journal, October 2015


Black hole binary dynamics from the double copy and effective theory
text, January 2019


The effective field theorist’s approach to gravitational dynamics
journal, May 2016


The tune of love and the nature(ness) of spacetime : The tune of love and the
journal, September 2016


Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering
journal, April 2019


The simplest massive S-matrix: from minimal coupling to black holes
journal, April 2019

  • Chung, Ming-Zhi; Huang, Yu-tin; Kim, Jung-Wook
  • Journal of High Energy Physics, Vol. 2019, Issue 4
  • DOI: 10.1007/JHEP04(2019)156

Highly spinning and aligned binary black hole merger in the Advanced LIGO first observing run
journal, July 2019


Gravitational spin Hamiltonians from the S matrix
journal, January 2015


Third post-Newtonian higher order ADM Hamilton dynamics for two-body point-mass systems
journal, June 1998


Scattering of spinning black holes from exponentiated soft factors
journal, September 2019

  • Guevara, Alfredo; Ochirov, Alexander; Vines, Justin
  • Journal of High Energy Physics, Vol. 2019, Issue 9
  • DOI: 10.1007/JHEP09(2019)056

Radiation reaction for spinning bodies in effective field theory. I. Spin-orbit effects
journal, October 2017


Radiation reaction for spinning bodies in effective field theory. II. Spin-spin effects
journal, October 2017


From boundary data to bound states
journal, January 2020


Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
journal, March 2019


Spin-multipole effects in binary black holes and the test-body limit
journal, March 2018


Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
text, January 2019

  • Foffa, Stefano; Porto Pereira, Rafael Alejandro; Rothstein, Ira
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
  • DOI: 10.3204/pubdb-2019-02862

Scattering of spinning black holes from exponentiated soft factors
text, January 2019


From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
text, January 2018


Black Hole Binary Dynamics from the Double Copy and Effective Theory
text, January 2019