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

Nigel T. Bishop·Roberto Gomez·Sascha Husa·Luis Lehner·Jeffrey Winicour
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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.

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Nigel T. Bishop, Roberto Gomez, Sascha Husa, Luis Lehner, Jeffrey Winicour. 2003-09-15. A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole. https://doi.org/10.1103/physrevd.68.084015

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