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Regular AdS$_3$ black holes from regularized Gauss-Bonnet coupling

Gokhan Alkac, Murat Mesta, Gonul Unal

TL;DR

This work constructs a three-dimensional bi-vector-tensor theory by regularizing the Gauss–Bonnet invariant in Weyl geometry with two Weyl vectors, yielding regular AdS$_3$ black holes possessing two primary hairs. Introducing a deformation parameter $\kappa$ produces a complementary regular AdS$_3$ black-hole family, with horizon structure controlled by hair parameters and $\kappa$. Coupling to Born–Infeld electrodynamics yields regular charged AdS$_3$ black holes, maintaining $\Lambda=\Lambda_0$ and enriching the parameter space. The results offer a tractable 3D model for exploring regular interiors, black-hole thermodynamics with hair, and potential AdS$_3$/CFT$_2$ entropy analyses, with prospects for microscopic entropy derivations and holographic insights.

Abstract

We obtain a three-dimensional bi-vector-tensor theory of the generalized Proca class by regularizing the Gauss-Bonnet invariant within the Weyl geometry. We show that the theory admits a regular AdS$_3$ black hole solution with primary hairs. Introducing a deformation in the theory, a different regular AdS$_3$ black hole solution is obtained. Charged generalizations of these solutions are given by coupling to Born-Infeld electrodynamics.

Regular AdS$_3$ black holes from regularized Gauss-Bonnet coupling

TL;DR

This work constructs a three-dimensional bi-vector-tensor theory by regularizing the Gauss–Bonnet invariant in Weyl geometry with two Weyl vectors, yielding regular AdS black holes possessing two primary hairs. Introducing a deformation parameter produces a complementary regular AdS black-hole family, with horizon structure controlled by hair parameters and . Coupling to Born–Infeld electrodynamics yields regular charged AdS black holes, maintaining and enriching the parameter space. The results offer a tractable 3D model for exploring regular interiors, black-hole thermodynamics with hair, and potential AdS/CFT entropy analyses, with prospects for microscopic entropy derivations and holographic insights.

Abstract

We obtain a three-dimensional bi-vector-tensor theory of the generalized Proca class by regularizing the Gauss-Bonnet invariant within the Weyl geometry. We show that the theory admits a regular AdS black hole solution with primary hairs. Introducing a deformation in the theory, a different regular AdS black hole solution is obtained. Charged generalizations of these solutions are given by coupling to Born-Infeld electrodynamics.

Paper Structure

This paper contains 10 sections, 43 equations, 2 figures.

Table of Contents

  1. Introduction
  2. 3d regularized Gauss--Bonnet invariant with two Weyl vectors
  3. Solution in [20] revisited
  4. Regular black hole solutions
  5. Undeformed theory ($\kappa=1$)
  6. Undeformed theory ($\kappa=1$) coupled to Born--Infeld electrodynamics
  7. Deformed theory ($\kappa\neq1$)
  8. Deformed theory ($\kappa\neq1$) coupled to Born--Infeld electrodynamics
  9. Conclusion
  10. Coupling to Maxwell's electrodynamics

Figures (2)

  • Figure 1: Figures showing the metric function and the corresponding curvature scalars for the undeformed theory. On the left, the plot of the metric function of the uncharged black hole in \ref{['metric_1']} is shown for a fixed set of parameters ($\kappa=1$, $m=1$, $\Lambda_0=-1$, and $\ell=0.5$) and for various values of the ratio $q_b/q_c$ (noted in the text boxes in the figure). The dashed line represents the BTZ black hole solution. On the right, metric function of the charged black hole in \ref{['metric_2']} is shown. The fixed parameters are the same with that of plot on the left, and the values of $q_b/q_c$ and $q_c$ varies as shown in the text boxes. The dotted line indicates the effect of a larger electric charge $q_e$ on the metric. In the insets, one can see the regularity of the curvature scalars explicitly.
  • Figure 2: Figures showing the metric function and the corresponding curvature scalars for the deformed theory. The same parameters that are used in Figure \ref{['fig1']} are implemented here as well as $q_b=1$. On the left, the effect of the deformation parameter $\kappa$ on the metric function \ref{['metric_3']} can be seen, giving rise to different horizon structures. The dotted line is for the extremal case corresponding to $\kappa=8.52$. The dashed line represents the BTZ black hole solution. On the right, the metric function \ref{['metric_4']} of the charged black hole is shown for different $\kappa$ values, and $q_e=1$ and $q_e=2$. The presence of the electric charge $q_e$ increases the required $\kappa$ value for the extremal solution to 12.05.