Rotation Effects and The Gravito-Magnetic Approach

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. 1 Gravito-Magnetic Aharonov-Bohm Effect Let 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”. The projected equation can be written in the form[4] D̂p̃i dT = mẼ i +mγ0 ( ṽ c × B̃G )