Quasilocal contribution to the gravitational self-force -: art. no. 024036

The gravitational self-force on a point particle moving in a vacuum background space-time can be expressed as an integral over the past world line of the particle, the so-called tail term. In this paper, we consider that piece of the self-force obtained by integrating over a portion of the past world line that extends a proper time Deltatau into the past, provided that Deltatau does not extend beyond the normal neighborhood of the particle. We express this quasilocal piece as a power series in the proper time interval Deltatau. We argue from symmetries and dimensional considerations that the O(Deltatau(0)) and O(Deltatau) terms in this power series must vanish, and compute the first two nonvanishing terms which occur at O(Deltatau(2)) and O(Deltatau(3)). The coefficients in the expansion depend only on the particle's four velocity and on the Weyl tensor and its derivatives at the particle's location. The result may be useful as a foundation for a practical computational method for gravitational self-forces in the Kerr space-time, in which the portion of the tail integral in the distant past is computed numerically from a mode-sum decomposition.