Canonical-Ensemble Stability of the Quantum Oppenheimer-Snyder Black-Hole Exterior

RESUMO

We study the local canonical thermodynamics of the quantum Oppenheimer--Snyder (qOS) black-hole exterior previously obtained from loop quantum cosmology. The spacetime is adopted from the literature; no new black-hole solution, regular extension, or singularity-resolution mechanism is claimed here. At fixed quantum parameter $\alpha$, we rewrite the outer horizon in a dimensionless form and obtain exact expressions for the mass, Hawking temperature, entropy, and heat capacity. These expressions reproduce the logarithmic entropy term and the heat-capacity divergence reported in earlier analyses. We then place those results in an explicit, regulated canonical-ensemble framework. The off-shell canonical action has a local minimum on a near-extremal branch with positive heat capacity and a local maximum on a large-black-hole branch with negative heat capacity. The two saddles merge at $r_h/\sqrt{\alpha}=\sqrt{(4+2\sqrt{7})/3}$, where the temperature is maximal and the heat capacity diverges. Because the asymptotically flat partition function is not normalizable without boundary data, this divergence is interpreted as a Davies-type local stability transition, not by itself as a global first-order phase transition. The principal contribution of this work is therefore a transparent canonical-saddle organization of known qOS thermodynamic results, together with a precise statement of its domain and limitations.