A Simple, Direct Finite Differencing of the Einstein Equations

We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a source for these wave equations. We demonstrate that this splitting method allows for the accurate simulation of compact objects, with gravitational field strengths less than or equal to those of neutron stars. This method could thus provide a straightforward path for general relativistic effects to be added to astrophysics simulations, such as in core collapse, accretion disks, and extreme mass ratio systems.