Classical black hole scattering from a worldline quantum field theory

Gustav Mogull (Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala, 75108, Sweden; Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, Berlin, D-12489, Germany; Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, Potsdam, D-14476, Germany) ; Jan Plefka (Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, Berlin, D-12489, Germany) ; Jan Steinhoff (Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, Potsdam, D-14476, Germany)

A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field h μν (x) and position x i μ τ i $$ {x}_i^{\mu}\left({\tau}_i\right) $$ of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈h μv (k)〉 and 2PM two-body deflection Δ p i μ $$ \Delta {p}_i^{\mu } $$ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

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      "surname": "Steinhoff", 
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  "abstracts": [
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      "source": "Springer", 
      "value": "A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field h  \u03bc\u03bd (x) and position   <math> <msubsup> <mi>x</mi> <mi>i</mi> <mi>\u03bc</mi> </msubsup> <mfenced> <msub> <mi>\u03c4</mi> <mi>i</mi> </msub> </mfenced> </math>  $$ {x}_i^{\\mu}\\left({\\tau}_i\\right) $$  of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation \u2329h  \u03bcv (k)\u232a and 2PM two-body deflection   <math> <mi>\u0394</mi> <msubsup> <mi>p</mi> <mi>i</mi> <mi>\u03bc</mi> </msubsup> </math>  $$ \\Delta {p}_i^{\\mu } $$  from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 \u2192 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT."
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Published on:
05 February 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 2
Pages 1-43
DOI:
https://doi.org/10.1007/JHEP02(2021)048
arXiv:
2010.02865
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: