Radiative Evolution of Orbits Around a Kerr Black Hole

TL;DR

This paper introduces a straightforward method to model how generic orbits around a Kerr black hole evolve due to radiation, providing new formulas for key orbital parameters including the Carter constant.

Contribution

The paper presents a novel, simple approach for the radiative evolution of generic orbits around Kerr black holes, including a closed-form expression for the Carter constant evolution.

Findings

Recovered standard results for energy and angular momentum evolution.

Derived a closed expression for Carter constant evolution.

Applicable to scalar-field scenarios around Kerr black holes.

Abstract

We propose a simple approach for the radiative evolution of generic orbits around a Kerr black hole. For a scalar-field, we recover the standard results for the evolution of the energy $E$ and the azimuthal angular momentum $L_z$ . In addition, our method provides a closed expression for the evolution of the Carter constant $Q$.