Classical black hole scattering from a worldline quantum field theory

Abstract

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 hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ 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.

Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

“…(Radiation effects in the PM expansion have also been recently approached in e.g. [137][138][139][140][141]. )…”

Light-ray operators, detectors and gravitational event shapes

“…to study radiation in this context both using classical worldline calculations [48][49][50][51][52][53][54] and double copy techniques scattering amplitudes in the classical limit [55,56]. In addition several classical observables like the classical impulse [57], the radiation kernel [57] and the classical spin kick [35,58] were defined in full generality from from the classical limit of matrix elements of appropriate quantum operators.…”

A worldsheet for Kerr

“…A partial understanding of this NJ phenomenon is available in the context of scattering amplitudes. Although amplitudes are rooted in quantum field theory, in recent years there has been an explosion of interest in applications of amplitudes to classical physics [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. This is motivated by the applicability of the results for elastic and inelastic [45][46][47][48][49][50][51][52][53][54][55][56][57] gravitational scattering of two massive particles to gravitational-wave physics [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], as JHEP03(2021)201 well as by the search for the underlying principles behind the double-copy relationship between gauge theory and gravity…”