Selfinteraction and massive vector field in the Schwarzschild spacetime.
Abstract
Using a multipole expansion, we determine formally the massive vector field generated by a point source held fixed in the Schwarzschild spacetime. We prove that its limit, when the mass of the Proca field goes to zero, does not tend to the corresponding massless vector field. In this limit we evaluate the expression of the selfforce acting on the particle. The result is in accordance with that of Vilenkin, without the assumption that the point source is at a large distance from the horizon, that we extend to the case of a ReissnerNordström spacetime. We also investigate a further case: a point source within a spherical shell of matter for which the Proca field tends to the corresponding massless vector field.
 Publication:

General Relativity and Gravitation
 Pub Date:
 August 1985
 DOI:
 10.1007/BF00762627
 Bibcode:
 1985GReGr..17..783L
 Keywords:

 Black Holes (Astronomy);
 Electrostatics;
 Field Theory (Physics);
 Gravitation Theory;
 Schwarzschild Metric;
 SpaceTime Functions;
 Charged Particles;
 Mass Distribution;
 Multipolar Fields;
 Particle Interactions;
 Point Sources;
 ReissnerNordstrom Solution;
 Self Excitation;
 Vector Spaces;
 Astrophysics;
 Schwarzschild Black Holes