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Properties of black hole vortex in Einstein’s gravity

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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.

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Data Availability Statement

This manuscript have associated data in a data repository. [Authors’ comment: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.]

Notes

  1. The term compact-like refers to solitonic field configurations with a finite wavelength [43]. Generally, one uses compact-like structures in describing topological structures associated with particles and cosmological objects, see Refs. [43, 44].

  2. One can verify this statement by performing an analytical analysis around the origin, i.e., \(r=0\). In this case, we obtain \(\lim _{r\rightarrow 0}A(r)\simeq -\varLambda r^2+\mathcal {O}(r^2)\).

  3. One verifies this analysis in Sect. 2.2.1

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Acknowledgements

C. A. S. Almeida thanks to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Grant No. 309553/2021-0. F. C. E. Lima is grateful to Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), No. 88887.372425/2019-00. The authors thank the referee for his valuable review.

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  1. Departamento de Física - Campus do Pici, Universidade Federal do Ceará (UFC), C. P. 6030, Fortaleza, CE, 60455-760, Brazil

    F. C. E. Lima, A. R. P. Moreira & C. A. S. Almeida

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  1. F. C. E. Lima
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Lima, F.C.E., Moreira, A.R.P. & Almeida, C.A.S. Properties of black hole vortex in Einstein’s gravity. Eur. Phys. J. Plus 138, 429 (2023). https://doi.org/10.1140/epjp/s13360-023-04036-8

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