Quasi-Asimptotically Flat Spacetimes and Their ADM Mass

TL;DR

This paper introduces a new class of asymptotically flat spacetimes with a deficit solid angle, defines a finite ADM mass for them, and discusses its properties including coordinate independence and potential negativity.

Contribution

It provides a novel definition of ADM mass for quasi-asymptotically flat spacetimes with deficit angles, extending previous concepts.

Findings

The ADM mass is finite for these spacetimes.

The ADM mass coincides with the monopole parameter M.

The definition is coordinate independent and can be negative.

Abstract

We define spacetimes that are asymptotically flat, except for a deficit solid angle $\alpha$, and present a definition of their ``ADM'' mass, which is finite for this class of spacetimes, and, in particular, coincides with the value of the parameter $M$ of the global monopole spacetime studied by Vilenkin and Barriola . Moreover, we show that the definition is coordinate independent, and explain why it can, in some cases, be negative.