Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity

Abstract

We model pseudo-Finsler geometries, with pseudo-Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo-Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated nonlinear connection structures and theirs metrics are solutions of the field equations in general relativity or in generalized gravity theories with nonholonomic variables. We rewrite the Schwarzschild metric in Finsler variables and use it for generating new classes of locally anisotropic black holes and (or) stationary deformations to ellipsoidal configurations. There are analyzed the conditions when such metrics describe imbedding of black hole solutions into nontrivial solitonic backgrounds.

latex 2e. 38 pages, v3 revised and accepted by Int. J. Theor. Phys. (shorten, with a Glossary of terms requested by referee, new references)

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Cited by in corpus (5)

• Finsler geometry as a model for relativistic gravity
• Schwarzschild-like solutions in Finsler-Randers gravity
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies