Classical black hole scattering from a worldline quantum field theory

A bstract 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 xᵢμ(τᵢ) x i μ τ i 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 pᵢμ 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.