Dynamical Regge Calculus as Lattice Quantum Gravity

TL;DR

This paper introduces a hybrid lattice quantum gravity model combining dynamical triangulations and Regge calculus, enabling the study of topology change, black hole entropy, and fractal spacetime structures through numerical simulations.

Contribution

It presents a novel hybrid approach to lattice quantum gravity that incorporates topology change and lattice diffeomorphisms, with applications to black hole entropy and quantum spacetime geometry.

Findings

Numerical simulations show a hysteresis between two phases in 3D pure gravity.

The model reproduces results consistent with dynamical triangulations and Regge calculus.

Evidence of fractal structures in Euclidean time slices in the strong-coupling phase.

Abstract

We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean spacetime. In addition, lattice diffeomorphisms as invariance of the simplicial geometry are generated by certain elementary moves in the model. We attempt also a lattice-theoretic derivation of the black hole entropy using the symmetry. Furthermore, numerical simulations of 3D pure gravity are carried out,exhibiting a large hysteresis between two phases. We also measure geometric properties of Euclidean `time slice' based on a geodesic distance, resulting in a fractal structure in the strong-coupling phase. Our hybrid model not only reproduces numerical results consistent with those of dynamical triangulations and Regge calculus, but also opens a possibility of studying quantum black hole physics on the lattice.