Relativistic hydrodynamics in the presence of puncture black holes

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 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 test bed 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.