Thermodynamics of polymerized vacuum regular black holes in anti-de Sitter spacetime

Abstract

We derive a class of vacuum regular black holes inspired by effective loop quantum gravity dynamics and extend the construction to asymptotically anti-de Sitter spacetimes. The derivation is based on a deparameterized Lemaitre--Tolman--Bondi formulation, where an auxiliary dust field is introduced only to define an internal time and does not act as a matter source. In spherical symmetry, the dynamics reduces to a set of independent radial shells, giving rise to a factorized shell Hamiltonian and to a Birkhoff-type property: for a fixed reconstruction function and cosmological constant, the static geometry is uniquely determined by the mass. Within this framework, we establish the conditions for curvature regularity at the center and construct several regular black hole models with de Sitter cores and corresponding models with anti-de Sitter cores. We then study their thermodynamics in the extended phase space, using the Hawking--Page transition to compare the de Sitter- and anti-de Sitter-core branches and show that their quantitative differences arise from the deformation of the physical outer-horizon branch rather than from regularity alone.