P. Papadopoulos et Ja. Font, RELATIVISTIC HYDRODYNAMICS AROUND BLACK-HOLES AND HORIZON ADAPTED COORDINATE SYSTEMS - ART. NO. 024005, Physical review. D. Particles and fields, 5802(2), 1998, pp. 4005
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].