Special relativistic spherically symmetric Lagrangean hydrodynamics from General Relativity

Abstract

We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is, for the case of weak gravitational fields. Explicit formulae are presented which relate General Relativistic independent variables, Lagrangean mass coordinate and variables in the lab-frame. Conversion of one set of variables into another requires knowing the solution to the set of equations. These formulae allow one to translate the solution to the exact set in General Relativity into the form in which Special Relativistic solutions are usually obtained. This is applicable for comparison of SR-numerical simulations of collapses, GRBs and Supernovae explosions with more precise GR-simulations.