Gauge, Averaging, Parity, and Modesum Regularization in Gravitational Self-force

Previous treatments of gravitational self-force have relied on Lorenz-gauge Hadamard techniques (involving lengthy calculations) for both the derivation and the expression of the final result. I give a short derivation that nowhere involves the Lorenz gauge and that leads to an angle-average formula for the self-force that holds in any admissible gauge. For gauges that satisfy a parity condition given by Regge and Teitelboim to ensure that their Hamiltonian center of mass is well-defined, the result simplifies to a simple average of the bare force. Remarkably, the parity condition also allows one to show that all such gauges share the same ``mode sum regularization parameters''. Since both the Lorenz gauge and a radiation gauge of Kerr (Keidl,Shah,Friedman,Kim,Price) satisfy the parity condition, existing Lorenz-gauge mode sum regularization results may be employed in radiation gauge calculations.