Nonholonomic Ricci Flows, Exact Solutions in Gravity, and Symmetric and Nonsymmetric Metrics

TL;DR

This paper demonstrates that nonholonomic Ricci flows of (pseudo) Riemannian metrics can produce nonsymmetric metrics, providing explicit examples and solutions relevant to general relativity.

Contribution

It proves that nonholonomic Ricci flows lead to nonsymmetric metrics and constructs explicit solutions deforming known symmetric metrics in gravity.

Findings

Ricci flows can generate nonsymmetric metrics from symmetric ones

Explicit solutions for deformations of Taub NUT, Schwarzschild, and wave metrics

Nonholonomic constraints influence metric evolution in gravity

Abstract

We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general relativity). There are constructed and analyzed three classes of solutions of Ricci flow evolution equations defining nonholonomic deformations of Taub NUT, Schwarzschild, solitonic and pp--wave symmetric metrics into nonsymmetric ones.