AXIOMATIC APPROACH TO ELECTROMAGNETIC AND GRAVITATIONAL-RADIATION REACTION OF PARTICLES IN CURVED SPACETIME

The problem of determining the electromagnetic and gravitational ''sel f-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ''comparison axiom,'' which states that whenever two particles of t he same charge e have the same magnitude of acceleration, the differen ce in their self-force is given by the ordinary Lorentz force of the d ifference in their (suitably compared) electromagnetic fields. We ther eby derive an expression for the electromagnetic self-force which agre es with that of DeWitt and Brehme as corrected by Hobbs. Despite sever al important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the grav itational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entire ly from a ''tail term,'' in agreement with recent results of Mino et a l. Throughout the paper, we take the view that ''point particles'' do not make sense as fundamental objects, but that ''point particle equat ions of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size bu t also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are gi ven by considering the limiting behavior of the self-force on extended bodies.