Holographic explorations of regular black holes in pure gravity

A bstract It has been recently established in Phys. Lett. B 861 (2025) 139260 that asymptotically flat black holes exist in pure gravity theories in dimension greater than four. We extend this result to asymptotically five dimensional 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 α ′3 W 4 correction of Type IIB supergravity on A₅ A 5 × S 5 as a series of QT terms. As anticipated in JHEP 11 (2019) 062, due to the presence of a bared AdS radius L, the perturbative field redefinition renormalizes Newton’s constant by an additive term of the form α ′3 L −6 R and induces lower order terms of the form ^ 3L^-4R² α ′ 3 L − 4 R 2 and ^ 3L^-2R³ α ′ 3 L − 2 R 3, both of which can be simultaneously written as QT terms, without spoiling the structure of the highest curvature term of the form ^ 3R⁴ α ′ 3 R 4. Before finishing, beyond holography, we also provide an extended thermodynamic setup, that via variations of the dimensionful α and L, allow obtaining the Euler relation between finite thermodynamical quantities for the black hole of the theory.