Mode-sum Regularization Research Articles

Self-force on a scalar particle in spherically symmetric spacetime via mode-sum regularization: Radial trajectories

Recently, we proposed a method for calculating the ``radiation reaction'' self-force exerted on a charged particle moving in a strong field orbit in a black hole spacetime. In this approach, one first calculates the contribution 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 regularize the (otherwise divergent) sum over modes. This involves the derivation of certain regularization parameters using local analysis of the (retarded) Green's function. In the present paper we present a detailed formulation of this mode-sum regularization scheme for a scalar charge on a class of static spherically-symmetric backgrounds (including, e.g., the Schwarzschild, Reissner-Nordstr\"{o}m, and Schwarzschild-de Sitter spacetimes). We fully implement the regularization scheme for an arbitrary radial trajectory (not necessarily geodesic) by explicitly calculating all necessary regularization parameters in this case.

Self-force on a particle in orbit around a black hole

We study the self-force acting on a scalar charge in uniform circular motion around a Schwarzschild black hole. The analysis is based on a direct calculation of the self-force via mode decomposition, and on a regularization procedure based on Ori's mode-sum regularization prescription. We find the four self-forces at arbitrary radii and angular velocities (both geodesic and nongeodesic), in particular near the black hole, where general-relativistic effects are strongest, and for fast motion. We find the radial component of the self-force to be repulsive or attractive, depending on the orbit.

Mode sum regularization approach for the self-force in black hole spacetime

We present a method for calculating the self-force (the ``radiation reaction force'') acting on a charged particle moving in a strong field orbit in black hole spacetime. In this approach, one first calculates the contribution to the self-force due to each multipole mode of the particle's field. Then, the sum over modes is evaluated, subject to a certain regularization procedure. Here we develop this regularization procedure for a scalar charge on a Schwarzschild background, and present the results of its implementation for radial trajectories (not necessarily geodesic).

Self-force on static charges in Schwarzschild spacetime

We study the self-forces acting on static scalar and electric test charges in the spacetime of a Schwarzschild black hole. The analysis is based on a direct, local calculation of the self-forces via mode decomposition and on two independent regularization procedures: a spatially extended particle model method and on a mode-sum regularization prescription. In all cases we find excellent agreement with the known exact results.