Thermodynamics of polymerized vacuum regular black holes in anti-de Sitter spacetime
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 Lema\^itre--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 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, with particular emphasis on the Hawking--Page transition. For the class of models considered, the dominant transition is of Hawking--Page type, determined by the crossing of the black hole free energy with the corresponding thermal-AdS background. The regularization affects the quantitative transition temperature by deforming the physical outer-horizon branch, including its endpoint structure. In the large anti-de Sitter radius regime, the de Sitter core solutions exhibit a higher Hawking--Page temperature than their anti-de Sitter-core counterparts, while the ordering can be modified close to the lower admissible range of the AdS scale. Thus, the thermodynamic differences between the two classes are not a consequence of regularity alone, but arise from how the core deformation modifies the horizon branch relative to the thermal-AdS reference background.