Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes

By Arnau Koemans Collado, Paolo Di Vecchia, R. Russo. Physical Review D, 2019

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In this paper we study the two-body gravitational scattering of massive scalars with different masses in general spacetime dimensions. We focus on the Regge limit (eikonal regime) of the resulting scattering amplitudes and discuss how to extract the classical information representing the scattering of two black holes. We derive the leading eikonal and explicitly show the resummation of the first leading energy contribution up to second order in Newton's gravitational constant. We also calculate the subleading eikonal showing that in general spacetime dimensions it receives a non-trivial contribution from the box integral. From the eikonal we extract the two-body classical scattering angle between the two black holes up to the second post-Minkowskian order (2PM). Taking various probe-limits of the two-body scattering angles we are able to show agreement between our results and various results in the literature. We highlight that the box integral also has a log-divergent (in energy) contribution at subsubleading order which violates perturbative unitarity in the ultra-relativistic limit. We expect this term to play a role in the calculation of the eikonal at the 3PM order.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f888fcd35a92bb72e33af8dd92e2f37cd510764d

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Citations in the corpus

Radiative contribution to classical gravitational scattering at the third order in G (2020, methodology): “[14] A.”
Post-Minkowskian effective field theory for conservative binary dynamics (2020, unknown): “[3, 62–91].”
Universality of ultra-relativistic gravitational scattering (2020, methodology): “This was also shown [13] to be the case for non-vanishing(5) m1,2.”
From boundary data to bound states (2019, background): “It would be also interesting to understand the connection with the eikonal phase [56].”
Classical gravitational scattering from a gauge-invariant double copy (2021, background): “16) of [117], which was obtained from the probe approximation of the deflection angle of a massive particle in the background of a Schwarzschild black hole in D dimensions.”
Post-Minkowskian Hamiltonians in general relativity (2019, background): “[26] A.”
Classical and quantum scattering in post-Minkowskian gravity (2019, methodology): “[19–23], and at the third post-Minkowskian (3PM) level (i.”