Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes

TL;DR

This paper develops a formalism for relativistic hydrodynamics applicable on both spacelike and null surfaces, with a spherical symmetry implementation tested on various scenarios including black hole accretion.

Contribution

It introduces a new formulation of relativistic hydrodynamics on null and spacelike hypersurfaces with explicit characteristic speeds, and provides a spherical symmetry implementation with multiple tests.

Findings

Successful simulation of fluid dynamics on null surfaces.

Accurate modeling of black hole accretion processes.

Versatile formalism applicable to dynamic spacetimes.

Abstract

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algorithm is tested in a number of different situations, predisposing for a range of possible applications. We consider the Riemann problem for a polytropic gas, with initial data given on a retarded/advanced time slice of Minkowski spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid evolution on dynamic background include constant density and TOV stars sliced along the radial null cones. Finally, we consider the accretion of self-gravitating matter onto a central black hole and the ensuing increase in the mass of the black hole horizon.