Black hole in Nielsen-Olesen vortex

TL;DR

This paper explores the formation and thermodynamics of black holes in (2+1)-dimensional gravity coupled with a Nielsen-Olesen vortex, revealing how magnetic vortices influence black hole temperature and thermodynamic laws.

Contribution

It provides the first detailed analysis of classical vortex solutions interacting with gravity and their role in black hole formation and thermodynamics in (2+1) dimensions.

Findings

Vortex solutions can lead to black hole formation in (2+1) dimensions.

Magnetic vortices alter the Hawking temperature of the black hole.

The first law of thermodynamics is modified by scalar and gauge fields in this context.

Abstract

In this article, we calculate the classical vortex solution of a spontaneously broken gauge theory interacting with gravity in (2+1)-dimension. We also calculate the conditions for the formation of a (2+1)-dimensional black hole due to magnetic vortex (a Nielsen-Olesen vortex). The semiclassical Hawking temperature for this black hole is calculated, where we see that the temperature of a BTZ black hole increases or decreases without changing the size of the horizon if we insert the magnetic vortex fields in the black hole. Finally, the first law of black hole thermodynamics is described for this particular solution, which shows that the additional work terms from the scalar and gauge fields compensate the change in the temperature relative to its usual value for the BTZ solution.