Radiation Reaction on Moving Particles in General Relativity

Abstract

A particle in the vicinity of a Schwarzschild black hole is known to trace a geodesic of the Schwarzschild background, to a first approximation. If the interaction of the particle with its own field (scalar, electromagnetic or gravitational) is taken into account, the path is no longer a background geodesic and the self-force that the particle experiences needs to be taken into consideration. In this dissertation, a recently proposed method for the calculation of the self-force is implemented. According to this method the self-force comes from the interaction of the particle with the Regular-Remainder scalar field, electromagnetic potential or metric perturbation. That Regular-Remainder is obtained by subtracting the Singular part (which exerts no force) from the retarded scalar field, electromagnetic potential of metric perturbation generated by the moving particle. First, the Singular scalar fields, electromagnetic potentials and metric perturbations are calculated for different sources moving in a Schwarzschild background. For that, the Thorne-Hartle-Zhang coordinates in the vicinity of the moving source are used. Then a mode-sum regularization method initially proposed for the direct scalar field is followed, and the regularization parameters for the singular part of the scalar field and for the first radial derivative of the singular part of the self-force are calculated. Also, the numerical calculation of the retarded scalar field for a particle moving on a circular geodesic in a Schwarzschild spacetime is presented. Finally, the self-force for a scalar particle moving on a circular Schwarzschild orbit is calculated and some results about the effects of the self-force on the orbital frequency of the circular orbit are presented.