Rotation Effects and The Gravito-Magnetic Approach

Abstract

Gravito-electromagnetism is somewhat ubiquitous in relativity. In fact, there are many situations where the effects of gravitation can be described by formally introducing "gravito-electric" and "gravito-magnetic" fields, starting from the corresponding potentials, in analogy with the electromagnetic theory[1],[2] (see also A. Tartaglia's contribution to these proceedings). The "many faces of gravito-electromagnetism" [3] are related to rotation effects in both approximated and full theory approaches. Here we show that, by using a 1+3 splitting, relativistic dynamics can be described in terms of gravito-electromagnetic (GEM) fields in full theory. On the basis of this formalism, we introduce a "gravito-magnetic Aharonov-Bohm effect", which allows to interpret some rotation effects as gravito-magnetic effects. Finally, we suggest a way for measuring the angular momentum of celestial bodies by studying the gravito-magnetic effects on the propagation of electromagnetic signals. Gravito-Magnetic Aharonov-Bohm EffectLet a physical reference frame (PRF) be defined by a time-like congruence Γ of world-lines of particles constituting the 3-dimensional reference frame.[4] The motion of free particles relative to Γ can be described by projecting the equation of motion onto the 3-space of the PRF by means of the "natural splitting". in terms of the GEM fieldsẼ G ,B G . In other words, the dynamics of particles, relative to the reference frame Γ, is described in terms of motion under the action 1 We refer to the projection technique developed by Cattaneo: see [4] and references therein.