# Perturbative Approach to an orbital evolution around a Supermassive black hole

## TL;DR

This paper develops a perturbative method to accurately determine the orbital evolution of a small mass particle around a Kerr black hole, accounting for radiation reaction effects using a novel field approach.

## Contribution

It introduces a perturbative approach utilizing the half-advanced minus half-retarded field to compute radiation reaction forces in black hole orbital dynamics.

## Key findings

- Half-advanced minus half-retarded field yields correct radiation reaction force.
- Method accurately predicts small deviations from geodesic motion.
- Applicable to orbital evolution around Kerr black holes.

## Abstract

A charge-free, point particle of infinitesimal mass orbiting a Kerr black hole is known to move along a geodesic. When the particle has a finite mass or charge, it emits radiation which carries away orbital energy and angular momentum, and the orbit deviates from a geodesic. In this paper we assume that the deviation is small and show that the half-advanced minus half-retarded field surprisingly provides the correct radiation reaction force, in a time-averaged sense, and determines the orbit of the particle.