New methods for approximating general relativity in numerical simulations of stellar core collapse

We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented. Such an effective relativistic potential can be used in an otherwise standard Newtonian hydrodynamic code. An alternative approximation of general relativity is the assumption of conformal flatness for the three-metric, and its extension by adding second post-Newtonian order terms. Using a code which evolves the coupled system of metric and fluid equations, we apply the various approximation methods to numerically simulate axisymmetric models for the col…