Lorentzian Gromov Hausdorff theory as a tool for quantum gravity kinematics

TL;DR

This paper explores Lorentzian Gromov Hausdorff theory as a promising mathematical framework for understanding the kinematics of quantum gravity, emphasizing its potential in Lorentzian approaches like causal set theory.

Contribution

It introduces Lorentzian Gromov Hausdorff theory as a novel tool for quantum gravity kinematics, highlighting its relevance for Lorentzian spacetime models.

Findings

Lorentzian Gromov Hausdorff theory provides a diffeomorphism invariant framework.

The theory is relevant for causal set theory and Lorentzian dynamical triangulations.

Potential of the theory to unify classical and quantum gravity approaches.

Abstract

This thesis start by a review of different approaches to classical and quantum gravity. The main theme is Lorentzian Gromov Hausdorff theory which is an active diffeomorphism invariant theory on the space of Lorentz spaces (think about globally hyperbolic spacetimes). It is argued why such theory might be of significant importance for Lorentzian approaches to quantum gravity such as causal set theory and Lorentzian dynamical triangulations