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AdS3 black holes with primary Proca hair from a regularized Gauss-Bonnet coupling

Gökhan Alkaç1,*, Murat Mesta2,†, and Gönül Ünal3,‡

  • 1Department of Aerospace Engineering, Faculty of Engineering, At𝚤l𝚤m University, 06836 Ankara, Türkiye
  • 2Department of Electrical and Electronics Engineering, Faculty of Engineering, At𝚤l𝚤m University, 06836 Ankara, Türkiye
  • 3Program of Biomedical Engineering, Faculty of Engineering, Başkent University, 06790 Ankara, Türkiye

  • *Contact author: alkac@mail.com
  • †Contact author: murat.mesta@atilim.edu.tr
  • ‡Contact author: gunalmesta@baskent.edu.tr
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Phys. Rev. D 112, 084055 – Published 22 October, 2025

DOI: https://doi.org/10.1103/1ws1-x8z3

Abstract

We construct a consistent three-dimensional Einstein-Gauss-Bonnet theory as a vector-tensor theory within the generalized Proca class by employing a regularization procedure based on the Weyl geometry, which was introduced recently by Charmousis, Fernandes, and Hassaine [Phys. Rev. D 111, 124008 (2025).]. We then obtain an asymptotically Anti-de Sitter (AdS3), static, and circularly symmetric black hole solution with primary Proca hair. Afterward, we investigate the effect of the scalar-tensor Gauss-Bonnet coupling constructed previously by different regularization schemes. We further generalize these solutions by incorporating an electric charge. As special cases, we find a regular black hole solution in addition to charged and uncharged stealth Banados-Teitelboim-Zanelli black hole solutions.

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Phys. Rev. D 112, 084055– Published 22 October, 2025
  • Received 13 August 2025
  • Accepted 29 September 2025
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