Simulating extreme-mass-ratio systems in full general relativity

TL;DR

This paper presents a novel numerical method for simulating extreme-mass-ratio systems in full general relativity, enabling efficient and accurate modeling of phenomena like stars falling into supermassive black holes.

Contribution

The authors introduce a background subtraction technique that improves the efficiency of simulating high mass ratio systems in Einstein's equations.

Findings

Successfully modeled a star infall into a supermassive black hole with mass ratios ≥ 10^6

Computed tidal deformation and gravitational wave emission during infall

Gravitational wave results closely match point-particle predictions

Abstract

We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract off its contribution to the truncation error, thereby more efficiently achieving a desired level of accuracy. We demonstrate the method by applying it to the radial infall of a solar-type star into supermassive black holes with mass ratios $\geq 10^6$. The self-gravity of the star is thus consistently modeled within the context of general relativity, and the star's interaction with the black hole computed with moderate computational cost, despite the over five orders of magnitude difference in gravitational potential (as defined by the ratio of mass to radius). We compute the tidal deformation of the star during infall, and the gravitational wave emission, finding the latter is close to the prediction of the point-particle limit.