Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes - art. no. 024015

We introduce a formulation of Eulerian general relativistic hydrodynamics w hich is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic s peeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algor ithm is tested in a number of different situations, predisposing for a rang e of possible applications. We consider the Riemann problem for a polytropi c gas, with initial data given on a retarded or advanced time slice of Mink owski spacetime. We compute perfect fluid accretion onto a Schwarzschild bl ack hole spacetime using ingoing null Eddington-Finkelstein coordinates. Te sts of fluid evolution on dynamic background include constant density and T olman-Oppenheimer-Volkoff 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.