A positive mass theorem for two spatial dimensions

TL;DR

This paper shows that a positive mass theorem analogue in 2D general relativity follows directly from the Gauss-Bonnet theorem, with the spatial slice being diffeomorphic to the plane.

Contribution

It establishes a simple proof of the positive mass theorem in two spatial dimensions using classical differential geometry.

Findings

Positive mass theorem analogue holds in 2D GR

Spatial slice is diffeomorphic to 2

Proof relies on Gauss-Bonnet theorem

Abstract

We observe that an analogue of the Positive Mass Theorem in the time-symmetric case for three-space-time-dimensional general relativity follows trivially from the Gauss-Bonnet theorem. In this case we also have that the spatial slice is diffeomorphic to $\Real^2$.