Properties of black hole vortex in Einstein's gravity

TL;DR

This paper studies how matter and gauge fields affect black hole vortex solutions in AdS$_3$ spacetime, revealing how field configurations influence metric functions, mass, and temperature of the black hole vortex.

Contribution

It introduces a detailed analysis of black hole vortex solutions with solitonic matter fields, highlighting the effects of field compactification and cosmological constant on their properties.

Findings

Black hole solutions appear for horizon radius around 1.5.

Compact-like field configurations lead to linearized metric behavior.

Black hole mass increases with more negative cosmological constant.

Abstract

We investigate the influence of the matter field and the gauge field on the metric functions of the AdS$_3$ spacetime of the Maxwell-Higgs model. By considering a matter field with a solitonic profile with the ability to adjust the field variable from kink to compact-like configurations, the appearance of black hole solutions is noticed for an event horizon at $r_{+} \approx 1.5$. An interesting result is displayed when analyzing the influence of matter field compactification on the metric functions. As we obtain compact-like field configurations the metric functions tend to a ``linearized behavior''. However, the compactification of the field does not change the structure of the horizon of the magnetic black hole vortex. With the ADM formalism, the mass of the black hole vortex is calculated, and its numerical results are presented. By analyzing the so-called ADM mass, it is observed that the mass of the black hole vortex increases as the cosmological constant becomes more negative, and this coincides with the vortex core becoming smaller. Nonetheless, this mass tends to decrease as the solitonic profile of the matter field becomes more compacted. Then, the black hole temperature study is performed using the tunneling formalism. In this case, it is perceived that the cosmological constant, and the $\alpha$-parameter, will influence the Bekenstein-Hawking temperature. In other words, the temperature of the structure increases as these parameters increase.