RELATIVISTIC HYDRODYNAMICS AROUND BLACK-HOLES AND HORIZON ADAPTED COORDINATE SYSTEMS - ART. NO. 024005

Despite the fact that the Schwarzschild and Kerr solutions for the Ein stein equations, when written in standard Schwarzschild and Boyer-Lind quist coordinates, present coordinate singularities, all numerical stu dies of accretion flows onto collapsed objects have been widely using them over the years. This approach introduces conceptual and practical complications in places where a smooth solution should be guaranteed, i.e., at the gravitational radius. In the present paper, we propose a n alternative way of solving the general relativistic hydrodynamic equ ations in background (fixed) black hole spacetimes. We identify classe s of coordinates in which the (possibly rotating) black hole metric is free of coordinate singularities at the horizon, independent of time, and admits a spacelike decomposition. In the spherically symmetric, n on-rotating case, we re-derive exact solutions for dust and perfect fl uid accretion in Eddington-Finkelstein coordinates, and compare them w ith numerical hydrodynamic integrations. We perform representative axi symmetric computations. These demonstrations suggest that the use of t hose coordinate systems carries significant improvements over the stan dard approach, especially for higher dimensional studies. [S0556-2821( 98)00814-5].