A new formulation of general-relativistic hydrodynamic equations using primitive variables

Abstract We present the derivation of hydrodynamical equations for a perfect fluid in General Relativity, within 3 + 1 decomposition spacetime framework, using only primitive variables. Primitive variables are opposed to conserved variables, as defined widely used Valencia formulation same equations. The derived covariant way, so that they can be describe any configuration fluid. Once derived, tested numerically. implement them an evolution code spherically symmetric self-gravitating compact objects. uses pseudospectral methods both metric and hydrodynamics. First, convergence tests performed, then frequencies radial modes polytropes recovered with without Cowling approximation, finally performance our black hole collapse migration described. results comparison reference core-collapse neutron star oscillations suggests not handle very strong gravitational fields, but also this new helps gaining significant amount computational time simulations smooth flows Relativity.