Steven A. Fromm, Vassilios Mewes, O. E. Bronson Messer, Eric J. Lentz, W. Raphael Hix, J. Austin Harris

We present formulations of effective potentials suitable for approximating general relativistic effects in Newtonian simulations of core-collapse supernovae. Assuming a spherically symmetric spacetime and a stress-energy tensor that includes both fluid and neutrino contributions, Eulerian and Lagrangian projections of the Einstein equations are made to determine general relativistic corrections to the Newtonian gravitational potential. We implement the effective potentials in both the Chimera and Flash-X codes, and perform a series of adiabatic and core collapse simulations. The results are compared to Newtonian and fully general relativistic simulations, as well as another widely used effective potential formulation. We find close agreement between our new effective potentials and the fully general relativistic results from multiple other codes.