Spin the black circle II: tidal heating and torquing of a rotating black hole by a test mass on generic orbits

TL;DR

This paper numerically studies horizon energy and angular momentum fluxes for particles orbiting Kerr black holes, revealing complex behaviors and proposing improved analytical models that better match numerical data, especially in strong-field regimes.

Contribution

The work introduces a new factorized, resummed analytical model for horizon fluxes that accurately predicts superradiant onset and improves upon existing post-Newtonian approximations.

Findings

Numerical fluxes show multiple peaks and sign changes for eccentric and hyperbolic orbits.

The proposed model predicts superradiant onset frequency within 10% for over 73% of configurations.

Analytical models achieve 10% accuracy at large separations and low eccentricities, but deviate significantly in strong-field regimes.

Abstract

Horizon fluxes of energy and angular momentum are a key strong-field effect in the dynamics of black holes, encoding direct information about their nature. In this work, we present a numerical study of these fluxes for a test particle orbiting a Kerr black hole on equatorial geodesics, covering circular, eccentric, and hyperbolic trajectories across a wide range of orbital parameters and black hole spins. We reproduce known results for circular orbits and uncover a richer phenomenology for eccentric and hyperbolic ones: the instantaneous fluxes can exhibit multiple peaks and sign changes, indicating a complex interplay between superradiant and non-superradiant regimes. We then compare these results against existing analytical post-Newtonian expressions, exploring resummation strategies to improve their performance against numerical data. In particular, we propose a factorized and resummed representation of the horizon fluxes that predicts the onset frequency of the superradiant regime to within $10\%$ for $\gtrsim 73\%$ of configurations for both the energy and angular momentum fluxes. This representation exactly reduces to the circular limit by construction, independently of the perturbative order of the remaining analytical terms. For peak and orbit-averaged fluxes, the analytical models achieve acceptable accuracy -- with relative errors at the $10\%$ level or below -- at large separations and low eccentricities. However, they can exhibit deviations of $\sim \mathcal{O}(100\%)$ in the strong-field regime, motivating the need for improved flux prescriptions and further investigations.