Central charge and black hole entropy for regular extremal black-bounce spacetimes

Abstract

The Bekenstein-Hawking entropy, proportional to one quarter of the horizon area, is fundamental in black hole thermodynamics and can also be understood via the AdS/CFT correspondence, such as the 3D BTZ black hole and 2D CFT. In this work, we adopt the Kerr/CFT approach to analyze the central charge and black hole entropy for regular extremal black-bounce spacetimes, including the counterparts of the Kerr, Kerr-Newman, and Reissner-Nordström black holes. These spacetimes are free of curvature singularities at $r=0$. We derive the near horizon geometries of these spacetimes and find that they exhibit enhanced symmetry, namely SL$(2,\mathbb{R})\times \mathrm{U}(1)$ or SL$(2,\mathbb{R}) \times \mathrm{SO}(3)$. By imposing appropriate boundary conditions, we analyze their asymptotic symmetry groups, which contain diffeomorphisms as well as the $\mathrm{U}(1)_{\rm gauge}$ symmetry arising from the electromagnetic field. We then extract the central charge from the charge algebra and evaluate the left-moving temperature of the Frolov-Thorne vacuum. It is worth emphasizing that in the black-bounce Kerr-Newman case, the central charge from the electromagnetic contribution vanishes. Furthermore, in the black-bounce Reissner-Nordström case, we uplift the 4D geometry to a 5D configuration by incorporating a $\mathrm{U}(1)$ gauge fiber. Our results show that the microscopic entropy calculated from the Cardy formula is consistent with the Bekenstein-Hawking entropy. This agreement suggests that the Kerr/CFT approach remains valid for certain regular spacetimes without curvature singularities, thereby providing a microscopic statistical understanding of black hole entropy.