The gravitating $\sigma$ model in 2+1 dimensions: black hole solutions

TL;DR

This paper explores black hole solutions within the gravitating O(3) sigma model in 2+1 dimensions, revealing three distinct static black holes, including singular and non-singular types, and constructing multi-black hole configurations.

Contribution

It introduces new static and dynamical black hole solutions in the 2+1 dimensional sigma model, including non-singular and multi-black hole systems, expanding understanding of lower-dimensional gravity models.

Findings

Identified three types of static black holes, including BTZ-like and non-singular solutions.

Constructed static and dynamical multi-black hole configurations.

Established similarities between some solutions and higher-dimensional black holes.

Abstract

We derive and discuss black-hole solutions to the gravitating O(3) $\sigma$ model in (2+1) dimensions. Three different kinds of static black holes are found. One of these resembles the static BTZ black hole, another is completely free of singularities, and the last type has the same Penrose diagram as the (3+1)-dimensional Schwarzschild black hole. We also construct static and dynamical multi-black hole systems.