A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole

TL;DR

This paper introduces a numerical relativity method to simulate the evolution of spacetime with a massive particle orbiting a Schwarzschild black hole, treating the particle as a rigid body on a geodesic.

Contribution

It develops a novel computational approach combining full numerical relativity with a rigid body particle model in a characteristic formulation.

Findings

Successfully simulated a complete orbit near r=9M of a Schwarzschild black hole.

Demonstrated the code's capability to handle particle-black hole interactions.

Validated the method with test runs showing stable evolution.

Abstract

We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a non-zero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a rigid body whose center follows a geodesic. The necessary theoretical framework is developed and then implemented in a computer code that uses the null-cone, or characteristic, formulation of numerical relativity. The performance of the code is illustrated in test runs, including a complete orbit (near r=9M) of a Schwarzschild black hole.