Analytic self-force effects on radial infalling particles in the Schwarzschild spacetime: the radiated energy

TL;DR

This paper calculates the first-order self-force effects on the energy radiated by particles falling into a Schwarzschild black hole, providing foundational insights for future higher-order and extended analyses.

Contribution

It presents the first self-force accuracy computation of radiated energy for radially infalling particles, including scalar and massive cases, with Post-Newtonian validation.

Findings

Computed radiated energy at first self-force order for infalling particles.

Validated results with Post-Newtonian checks.

Outlined methods for higher-order and extended future computations.

Abstract

We compute, at the first self force accuracy level, the radiated energy from a radially infalling particle released from rest in a Schwarzschild spacetime. We examine both the cases of a scalar particle and that of a massive particle, in the context of gravitational perturbations. Our findings are accompanied by Post-Newtonian checks. In spite of the specific interest for this kind of computations, we outline the building blocks for future higher-order Post-Newtonian computations as well as for extending these results to other interesting situations out of the black hole case.