Violation of the Strong Equivalence Principle due to the self-force in a Kerr spacetime

Abstract

As is known, a charge in a gravitational field experiences a (gravitationally-induced) self-interaction force (“self-force”) only in curved space-times (in any reference frame), but not in the accelerated frames in flat spacetimes. Therefore, the presence of any self-force indicates, from a formal point of view, a violation of the Strong Equivalence Principle (SEP); as a result, “observability of the self-force in the validity domain of classical electrodynamics” (CE) means “observability of the related violation of SEP”. In this paper we investigate the observability of the self-force on a charge at rest on the symmetry axis in a Kerr spacetime, as recently calculated in a paper by the same authors, in the validity domain of CE. Analysis shows that, in the validity domain of CE, no effect of the self-force is observable outside the Schwarzschild radius. In contrast, some effect is observable for very large values of the angular momentum, in a small neighbourhood of the “turning point” (where a reversal of the tidal forces direction takes place), between the outer horizon and the Schwarzschild radius. This is the only case we have found where SEP fails because of the self-force.