Gravitational Self-Force Regularization in the Regge-Wheeler and Easy Gauges

Abstract

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 ODE, 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 $r_0=6M$ and $10^{-16}$ for an orbital radius of $r_0=10M$.