  We propose an approximation to general relativity that captures the main
gravitational effects of dynamical importance in supernovae. The conceptual
link between this formalism and the Newtonian limit is such that it could
likely be implemented in existing multidimensional Newtonian gravitational
hydrodynamics codes employing a Poisson solver. As a test of the formalism's
utility, we display results for rapidly rotating (and therefore highly
deformed) neutron stars.
