General Relativity and the Ricci Flow

TL;DR

This paper explores merging Ricci flow with the Hamilton-Jacobi equation in general relativity to address the problem of time in quantum gravity, proposing a novel theoretical approach.

Contribution

It introduces a new theoretical framework combining Ricci flow and Hamilton-Jacobi equations for quantum gravity research.

Findings

Proposes a unified equation for Ricci flow and Hamilton-Jacobi in GR

Suggests potential insights into the problem of time in quantum gravity

Lays groundwork for future mathematical and physical investigations

Abstract

In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature. As a step towards resolving the problem of time in quantum gravity, we attempt to merge the Ricci flow equation with the Hamilton-Jacobi equation for general relativity.