# The global monopole spacetime and its topological charge

## TL;DR

This paper derives the global monopole spacetime as an exact Einstein solution using a non-linear sigma model, explains the origin of its topological charge, and extends thermodynamic spacetime generation to include monopole charge.

## Contribution

It provides a new derivation of the global monopole spacetime without weak field approximation and clarifies the physical origin of its topological charge.

## Key findings

- Global monopole spacetime is an exact Einstein solution.
- The physical origin of the topological charge is identified.
- Thermodynamic laws are extended to spacetimes with monopole charge.

## Abstract

In this paper, we show that the global monopole spacetime is one of the exact solutions of Einstein equations by means of the method treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin in 1989. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally, we generalize the proposal which generates spacetime from thermodynamical laws to the case that spacetime with global monopole charge.