Scattering of a point mass by a Schwarzschild black hole: radiated energy and angular momentum

TL;DR

This paper computes the radiated energy and angular momentum from a point mass orbiting a Schwarzschild black hole using first-order self-force theory, combining PM and PN expansions, and provides new high-order analytical results.

Contribution

It introduces the first analytical expressions for radiative losses at 5PM order in the self-force framework, advancing the understanding of gravitational scattering.

Findings

Derived 7PN accurate flux expressions for energy and angular momentum.

Achieved $O(G^5)$ accuracy for radiated energy and $O(G^4)$ for angular momentum.

Provided a 5PM radiation-reacted scattering angle for the first time.

Abstract

The radiated energy and angular momentum from a point mass on a hyperbolic-like orbit about a Schwarzschild black hole are computed for the first time in the framework of the first-order self-force theory. The analytical expressions for the fluxes are obtained through the standard method of Mano, Suzuki and Takasugi in the form of combined post-Minkowskian (PM) and post-Newtonian (PN) expansions. The reached PM accuracy for the energy and angular momentum losses is $O(G^5)$ and $O(G^4)$, respectively, and 7PN for both. The radiative losses (energy, angular momentum and linear momentum) are currently known in PN-expanded form up to the (fractional) 3PN order [D. Bini et al., Phys. Rev. D \textbf{107}, 024012 (2023)]. Exact PM results valid for arbitrary values of the velocity are limited to $O(G^4)$ for the energy and $O(G^3)$ for the angular momentum. An exact expression for the radiated energy at $O(G^5)$ has been recently obtained in [M. Driesse et al., Nature \textbf{641}, 603-607 (2025)] in the first-order self force limit, whereas the $O(G^4)$ radiated angular momentum has been partially determined in [C. Heissenberg, Phys. Rev. D \textbf{111}, 126012 (2025)]. The results of this work are in agreement with the state of the art of both energy and angular momentum losses, also completing the knowledge of the 4PM radiated angular momentum up to the reached PN accuracy. The expressions for radiative losses are then used to get the 5PM radiation-reacted scattering angle, which should also serve as a cross-check of ongoing calculations by other methods.