Relativistic hydrodynamics in the presence of puncture black holes

TL;DR

This paper investigates the application of the moving puncture approach to simulate relativistic hydrodynamics around black holes, demonstrating successful evolution without excision and supporting its use in black hole-neutron star mergers.

Contribution

It extends the moving puncture method to relativistic hydrodynamics, showing it can handle matter without excision and validating its potential for binary systems.

Findings

Hydrodynamical equations evolve successfully without excision.

Exterior spacetime solutions are invariant to initial data inside the black hole.

Supports using the puncture approach for black hole-neutron star simulations.

Abstract

Many of the recent numerical simulations of binary black holes in vacuum adopt the moving puncture approach. This successful approach avoids the need to impose numerical excision of the black hole interior and is easy to implement. Here we wish to explore how well the same approach can be applied to moving black hole punctures in the presence of relativistic hydrodynamic matter. First, we evolve single black hole punctures in vacuum to calibrate our BSSN (Baumgarte-Shapiro-Shibata-Nakamura) implementation and to confirm that the numerical solution for the exterior spacetime is invariant to any ``junk'' (i.e., constraint-violating) initial data employed in the black hole interior. Then we focus on relativistic Bondi accretion onto a moving puncture Schwarzschild black hole as a numerical testbed for our high-resolution shock-capturing relativistic hydrodynamics scheme. We find that the hydrodynamical equations can be evolved successfully in the interior without imposing numerical excision. These results help motivate the adoption of the moving puncture approach to treat the binary black hole-neutron star problem using conformal thin-sandwich initial data.