Gravitational self-force regularization in the Regge-Wheeler and easy gauges

We present numerical results for the gravitational self-force and redshift invariant calculated in the Regge-Wheeler and easy gauges for circular orbits in a Schwarzschild background, utilizing the regularization framework introduced by Pound, Merlin, and Barack. The numerical calculation is performed in the frequency domain and requires the integration of a single second-order ordinary differential equation, greatly improving computation times over more traditional Lorenz gauge numerical methods. A sufficiently high-order, analytic expansion of the Detweiler-Whiting singular field is gauge transformed to both the Regge-Wheeler and easy gauges and used to construct tensor-harmonic mode-sum regularization parameters. We compare our results to the gravitational self-force calculated in the Lorenz gauge by explicitly gauge transforming the Lorenz gauge self-force to the Regge-Wheeler and easy gauges, and find that our results agree to a relative accuracy of 10−15 for an orbital radius of r0=6M and 10−16 for an orbital radius of r0=10M.