Nonholonomic Ricci Flows and Parametric Deformations of the Solitonic pp--Waves and Schwarzschild Solutions

Abstract

We study Ricci flows of some classes of physically valuable solutions in Einstein and string gravity. The anholonomic frame method is applied for generic off-diagonal metric ansatz when the field/ evolution equations are transformed into exactly integrable systems of partial differential equations. The integral varieties of such solutions, in four and five dimensional gravity, depend on arbitrary generation and integration functions of one, two and/ or three variables. Certain classes of nonholonomic frame constraints allow us to select vacuum and/or Einstein metrics, to generalize such solutions for nontrivial string (for instance, with antisymmetric torsion fields) and matter field sources. A very important property of this approach (originating from Finsler and Lagrange geometry but re-defined for semi-Riemannian spaces) is that new classes of exact solutions can be generated by nonholonomic deformations depending on parameters associated to some generalized Geroch transforms and Ricci flow evolution. In this paper, we apply the method to construct in explicit form some classes of exact solutions for multi-parameter Einstein spaces and their nonholonomic Ricci flows describing evolutions/ interactions of solitonic pp-waves and deformations of the Schwarzschild metric. We explore possible physical consequences and speculate on their importance in modern gravity.

arXiv commentlatex2e, 11pt, the variant accepted for EJTP

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Cited by in corpus (10)

• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• 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
• Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
• Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
• Nonholonomic Ricci Flows: Exact Solutions and Gravity
• 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