Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations

TL;DR

This paper explores coupling a point-like mass to four-dimensional quantum gravity within the causal dynamical triangulations framework, deriving classical volume profiles and discussing numerical implementation challenges.

Contribution

It introduces a method to couple a non-singular point mass to quantum gravity in CDT and compares classical volume profiles with pure gravity models.

Findings

Derived the spatial volume profile of Schwarzschild-de Sitter space in CDT

Identified bounds on mass for valid calculations due to coordinate caustics

Discussed numerical strategies for measuring volume profiles in matter-coupled CDT

Abstract

We present a possibility of coupling a point-like, non-singular, mass distribution to four-dimensional quantum gravity in the nonperturbative setting of causal dynamical triangulations (CDT). In order to provide a point of comparison for the classical limit of the matter-coupled CDT model, we derive the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued to an interior matter solution. The volume profile is calculated with respect to a specific proper-time foliation matching the global time slicing present in CDT. It deviates in a characteristic manner from that of the pure-gravity model. The appearance of coordinate caustics and the compactness of the mass distribution in lattice units put an upper bound on the total mass for which these calculations are expected to be valid. We also discuss some of the implementation details for numerically measuring the expectation value of the volume profiles in the framework of CDT when coupled appropriately to the matter source.