Self-force on a scalar particle in spherically symmetric spacetime via mode-sum regularization: Radial trajectories - art. no. 084027

Recently, we proposed a method for calculating the "radiation reaction'' se lf-force exerted on a charged particle moving in a strong field orbit in a black hole spacetime. In this approach, one first calculates the contributi on to the "tail'' part of the self-force due to each multipole mode of the particle's self-field. A certain analytic procedure is then applied to regu larize the (otherwise divergent) sum over modes. This involves the derivati on of certain regularization parameters using local analysis of the (retard ed) Green's function. In the present paper we present a detailed formulatio n of this mode-sum regularization scheme for a scalar charge on a class of static spherically symmetric backgrounds (including, e.g., the Schwarzschil d, Reissner-Nordstrom, and Schwarzschild-de Sitter spacetimes). We fully im plement the regularization scheme for an arbitrary radial trajectory (not n ecessarily geodesic) by explicitly calculating all necessary regularization parameters in this case.