Determination of the angular momentum of the Kerr black hole from equatorial geodesic motion

TL;DR

This paper introduces a method to determine a Kerr black hole's angular momentum by analyzing equatorial geodesic trajectories, using Hamiltonian dynamics and numerical simulations to accurately infer the black hole's spin from observational data.

Contribution

It provides a novel algebraic and numerical approach to estimate black hole angular momentum from trajectory data, improving accuracy and applicability over previous methods.

Findings

Successfully derived an algebraic equation for black hole angular momentum.

Developed a numerical code to solve the dynamical equations.

Achieved good agreement between inferred and input parameters in simulations.

Abstract

We present a method to determine the angular momentum of a black hole, based on observations of the trajectories of the bodies in the Kerr space-time. We use the Hamilton equations to describe the dynamics of a particle and present results for equatorial trajectories, obtaining an algebraic equation for the magnitude of the black hole's angular momentum. We tailor a numerical code to solve the dynamical equations and use it to generate synthetic data. We apply the method in some representative examples, obtaining the parameters of the trajectories as well as the black hole's angular momentum in good agreement with the input data.