Topology change in quantum gravity and Ricci flows

TL;DR

This paper models topology change in quantum gravity using Ricci flows, treating them as a statistical system where metrics represent microscopic states, and investigates this numerically starting from a wormhole with a scalar field.

Contribution

It introduces a novel perspective of Ricci flow as a statistical system for modeling topology change in quantum gravity, supported by numerical analysis.

Findings

Ricci flow can be interpreted as a statistical ensemble of microscopic states.

Numerical simulations show the evolution of a wormhole under Ricci flow.

The approach links geometric flows with quantum gravity phenomena.

Abstract

The topology change in quantum gravity is modeled by a Ricci flow. In this approach we offer to consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter $\lambda$ is a microscopical statistical state. The probability of every microscopical state is determined by the parameter $\lambda$. Numerically the Ricci flow starting from a static wormhole filled with a phantom Sine-Gordon scalar field is investigated.