Abstract. We have extended some high-resolution shock-capturing methods, designed recently to solve nonlinear hyperbolic systems of conservation laws, to the general-relativistic hydrodynamic system of equations and applied them to the study of the gravitational collapse of spherically symmetric configurations.

INTRODUCTION

Several topics are of current interest among astrophysicists working in the field of stellar collapse: (i) The equation of state for both subnuclear and supranuclear densities. Alongside the theoretical problems concerned here, there is also the technical problem of making both approaches consistent with each other, as well as sufficiently fast to compute in stellar collapse calculations (see Lattimer and Swesty, 1992). (ii) The coupling between neutrinos and matter in connection with the feasibility of the so-called delayed mechanism. (iii) The correct modelling of shocks in order to conserve total energy along the propagation of the shock formed in the collapse after bounce. In the last years, a part of our research has been addressed to this point.

In a previous paper (Martí et al., 1990, in the next MIM90) we have focussed on the shock formation and propagation such as it appears in the standard scenario of the prompt mechanism. In MIM90 we have undertaken Newtonian stellar collapse calculations with two codes: (i) A standard finite-difference scheme which uses an artificial viscosity technique. (ii) A Godunov-type method which uses a linearized Riemann solver. The initial model and the equation of state was kept fixed in order to be able to compare both methods directly.