Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics

Abstract

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/Ricci flow models with nontrivial torsion to configurations with the Levi-Civita connection is allowed in some specific physical circumstances by constraining the class of integral varieties for the Einstein and Ricci flow equations.

arXiv commentlatex2e, final variant to be published in IJMPA

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• The Entropy of Lagrange-Finsler Spaces and Ricci Flows
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in $R^2$ and Einstein Gravity Theories
• On Supersymmetric Geometric Flows and ${\mathcal{R}}^2$ Inflation From Scale Invariant Supergravity
• Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity
• Metric Compatible or Noncompatible Finsler-Ricci Flows
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations