  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.
