Holographic explorations of regular black holes in pure gravity

TL;DR

This paper extends the study of regular black holes to asymptotically Anti-de Sitter spacetimes using holography, analyzing phase transitions, quasinormal modes, and quark-antiquark potentials within a higher-curvature gravity framework.

Contribution

It introduces a class of higher-curvature Quasi-topological Lagrangians in pure gravity, enabling analytic solutions for regular black holes in AdS and their holographic duals.

Findings

Derived general formulas for regular black holes in AdS with higher-curvature terms.

Explored specific cases leading to Hayward, Dymnikova, and Bardeen-like black holes.

Connected supergravity corrections to Quasi-topological gravity series.

Abstract

It has been recently established in \textit{Phys.Lett.B 861 (2025) 139260} that regular, asymptotically flat black holes exist in pure gravity theories in dimension greater than four. We extend this result to asymptotically Anti-de Sitter spacetimes and perform bottom-up holographic explorations: Hawking-Page phase transitions, quasinormal modes of black holes providing decay times of excitations in the finite temperature conformal field theory and U-shaped string probes leading to the quark-antiquark potential in the dual field theory. The gravitational action contains a bared, negative cosmological constant and an Einstein-Hilbert term, supplemented by an infinite series of higher-curvature terms of the family known as Quasi-topological (QT) Lagrangians, leading to a lapse function in terms of infinite series which can be resumed to an analytic function for different coupling choices. The QT terms are defined as those satisfying a Birkhoff's theorem and possessing a holographic c-function, and exist at all orders in the curvature, for arbitrary dimension greater than four. Besides presenting the general formulae, we explore the physics of three specific cases leading to Hayward, Dymnikova and Bardeen-like regular black holes. We also found the field redefinition that permits recasting the $\alpha'^3 W^4$ correction of Type IIB supergravity on $\mathcal{A}_5\times S^5$ as a series of QT terms. Before finishing, beyond holography, we also provide an extended thermodynamic setup, that via variations of the dimensionful $\alpha$ and $L$, allow obtaining the Euler relation between finite thermodynamical quantities for the black hole of the theory.