Gravitational self force by mode sum regularization

We propose a practical scheme for calculating the local gravitational self-force experienced by a test mass particle moving in a black hole spacetime. The method—equally effective for either weak or strong field orbits—employs the mode-sum regularization schemepreviously developed for a scalar toy model. The starting point for the calculation, in this approach, is the formal expression for the regularized self-force derived by Mino et al. @Phys. Rev. D 55, 3457 ~1997!# Nand, independently, by Quinn and Wald @Phys. Rev. D 56, 3381 ~1997!#O, which involves a worldline integral over the tail part of the retarded Green’s function. This force is decomposed into multipole ~tensor harmonic! modes, whose sum is subjected to a carefully designed regularization procedure. This procedure involves an analytical derivation of certain ‘‘regularization parameters’’ by means of a local analysis of the Green’s function. This paper contains the following main parts: ~1! The