Nonlinear Connections and Nearly Autoparallel Maps in General Relativity

Details Nonlinear Connections and Nearly Autoparallel Maps in General Relativity Nonlinear Connections and Nearly Autoparallel Maps in General Relativity

2000-09-12

arxiv.org/abs/gr-qc/0009038v1

Gen.Rel.Grav. 35 (2003) 807-850

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

41 pages

Scientific paper

We apply the method of moving anholonomic frames, with associated nonlinear connections, in (pseudo) Riemannian spaces and examine the conditions when various types of locally anisotropic (la) structures (Lagrange, Finsler like and more general ones) could be modeled in general relativity. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formulate the theory of nearly autoparallel (na) maps and introduce the tensorial na-integration as the inverse operation to both covariant derivation and deformation of connections by na-maps. The problem of redefinition of the Einstein gravity theory on na-backgrounds, provided with a set of na-map invariant conditions and local conservation laws, is analyzed. There are illustrated some examples of generation of vacuum Einstein fields by Finsler like metrics and chains of na-maps.

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