Asymptotically Hyperbolic 3-Metric with Ricci flow foliation

TL;DR

This paper constructs asymptotically hyperbolic 3-metrics using Ricci flow foliations, extending previous flat metric approaches to hyperbolic settings in general relativity.

Contribution

It introduces a method to build asymptotically hyperbolic 3-metrics with Ricci flow foliation, expanding the scope of geometric constructions in relativity.

Findings

Successful construction of hyperbolic metrics with Ricci flow foliation

Analysis of the rigid case where Hawking mass equals total mass

Extension of flat metric techniques to hyperbolic geometry

Abstract

In general relativity, there have been a number of successful constructions for asymptotically flat metrics with a certain background foliation. In particular, C. -Y. Lin used a foliation by the Ricci flow on 2-spheres to establish an asymptotically flat extension and C. Sormani and Lin proved useful results with this extension. In this paper, we construct asymptotically hyperbolic 3-metrics with the Ricci flow foliation. We also study the rigid case when the Hawking mass of the inner surface of the manifold agrees with its total mass.