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 nonzero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a quasirigid 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.

• Received 16 January 2003

DOI:https://doi.org/10.1103/PhysRevD.68.084015