Studying quantum gravity via simplicial Lorentzian path integrals

Abstract

This thesis investigates the Lorentzian path integral as a framework for quantum gravity, focusing on how its off-shell causal structure shapes physical predictions. The work shows that different assumptions about causality strongly affect phenomena such as cosmological tunneling, black hole thermodynamics, and gravitational entropy. A central result is the discovery that certain off-shell causality violations in the Lorentzian path integral give rise to the Euclidean saddle points that dominate semiclassical calculations, providing a concrete mechanism through which Euclidean features emerge from fundamentally Lorentzian dynamics. To study these questions non-perturbatively, the thesis uses Regge calculus, a discrete version of General Relativity that makes Lorentzian path integrals computationally tractable. The framework enables detailed studies of two key settings: Euclidean de Sitter space and evaporating black holes. In the de Sitter case, Euclidean saddles are shown to govern both cosmological tunneling amplitudes and entropy-related state counting, requiring unusual off-shell geometries with singular causal structures. In the black hole context, the work develops a Regge-calculus approach to replica wormholes and reproduces the Page curve within a four-dimensional gravitational model that includes matter. Overall, the thesis advances both the conceptual understanding and computational treatment of Lorentzian quantum gravity, establishing Regge calculus as a powerful tool for studying quantum aspects of gravity.