Gravitoelectromagnetism: an Interface Between Our Space Plus Time Perspective of the Physical World and its Spacetime Description in General Relativity.
Abstract
Gravitoelectromagnetism provides for the first time a single mathematical framework where the various ways of splitting spacetime, and of reintroducing spatial gravitational forces into general relativity, can be compared and clarified. Within this framework, general relativity in its exact formulation can be recast in a form which is a nonlinear analogy of electromagnetism. At the most general level (congruence point of view) one identifies a congruence of observers' worldlines and decomposes spacetime into their local rest spaces and time directions. Any tensor field and tensorial equation can then be reduced to a set of spatial fields and spatial equations via the process of "measurement". Various spatial differential operators differentiating along spatial and temporal directions can be introduced, the latter being associated with different ways of "evolving" frames along the observer congruence. A direct application of these ideas leads to the introduction of gravitoelectromagnetic forces and fields which turn out to be directly related to the kinematical properties of the 4-velocity field of the observers, and to the spatial curvature. The congruence point of view can be anchored to the spacetime manifold via a coordinate system adapted to the "slicing" (hypersurfaces of constant time) and to the "threading" (lines of constant spatial coordinates). Identifying the threading with the observer congruence leads directly to the "threading point of view". Identifying the normal to the slicing with the 4-velocity of the observers, but describing the evolution along the threading, leads to the "slicing point of view". The congruence point of view has been used to find the most general solution to the problem of addition of accelerations in general relativity, and to separate the geodesic, space curvature and gravitomagnetic contributions to the gyroscope precession, without approximations. The role of the various spatial gravitational forces along the circular orbits of some known spacetime have been studied in the threading and slicing points of view. The question of the existence of a gyroscope gravitational Thomas precession has been analyzed, and the arbitrariness of the result has been related to the impossibility of defining univocally the gravitomagnetic field along a single worldline.
- Publication:
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Ph.D. Thesis
- Pub Date:
- January 1996
- Bibcode:
- 1996PhDT.........3C
- Keywords:
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- Physics: General, Physics: Astronomy and Astrophysics