Studying replica wormholes and the Page curve with simplicial quantum gravity

Abstract: The replica paradigm has emerged as a powerful tool for investigating the black hole information paradox, offering a semiclassical route to reproducing the Page curve and suggesting unitary evolution for evaporating black holes. However, existing analyses have relied on simplified models such as JT gravity, and mostly remain limited to the $n \to 1^+$ limit in Euclidean signature. This work develops a framework based on Quantum Regge Calculus (QRC) that provides a lattice-like approach to address these gaps. A triangulation scheme is introduced that accommodates both gravitational and radiation degrees of freedom, enabling explicit evaluation of the fundamental components of the Regge gravity and radiation actions in a spherically symmetric setting. The formulation naturally incorporates analytic continuation techniques to probe the role of complex saddles in Lorentzian signature. A proof-of-principle implementation is carried out within a controlled minisuperspace reduction, revealing semiclassical saddles in the $n \to 1^+$ limit that recover the Page transition. While significant challenges remain (including the definition of the discrete configuration space, ambiguities in the gravitational measure, and the treatment of asymptotic boundaries), the framework developed here provides a promising foundation for further progress. The results suggest that sufficiently refined QRC calculations could extend the replica approach beyond existing models.