Nonholonomic Ricci Flows: Exact Solutions and Gravity

Abstract

In a number of physically important cases, the nonholonomically (nonintegrable) constrained Ricci flows can be modelled by exact solutions of Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We develop two geometric methods for constructing such solutions: The first approach applies the formalism of nonholonomic frame deformations when the gravitational evolution and field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The second approach develops a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in a class of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. We also consider nonlinear superpositions of some mentioned classes of solutions in order to construct more general integral varieties of the Ricci flow and Einstein equations depending on infinite number of parameters and three/ four coordinates on four/ five dimensional (semi) Riemannian spaces.

latex2e, 11pt, 39 pages; title changed; typos corrected and updated references; for publication in EJTP

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Cited by in corpus (6)

• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Fractional Nonholonomic Ricci Flows
• Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
• Diffusion and Self-Organized Criticality in Ricci Flow Evolution of Einstein and Finsler Spaces
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity