Nonlinear connections and nearly autoparallel maps in general relativity. (English) Zbl 1026.83049
Summary: We apply the method of moving anholonomic frames with associated nonlinear connections to the (pseudo) Riemannian space geometry and examine the conditions when locally anisotropic structures (Finsler like and more general ones) could be modeled in the general relativity theory and/or Einstein-Cartan-Weyl extensions [S. L. Vacaru and H. Dehnen, Gen. Relativ. Gravitation 35, 209-250 (2003; Zbl 1016.83034)]. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formulate the theory of nearly autoparallel (na) maps generalizing the conformal transforms and formulate the Einstein gravity theory on na-backgrounds provided with a set of na-map invariant conditions and local conservation laws. There are illustrated some examples when vacuum Einstein fields are generated by Finsler like metrics and chains of na-maps.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 53B40 | Local differential geometry of Finsler spaces and generalizations (areal metrics) |
Citations:
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