Time and a physical Hamiltonian for quantum gravity

TL;DR

This paper develops a non-perturbative quantum gravity framework using dust as a natural time variable, resulting in a physical Hamiltonian that simplifies previous models and enables applications in cosmology and black hole physics.

Contribution

It introduces a novel non-perturbative quantization of gravity with dust, leading to a Hamiltonian without a square root, simplifying the theory and broadening its applications.

Findings

Hamiltonian is not a square root, simplifying calculations.

Provides a complete quantum gravity theory with matter coupling.

Enables applications to cosmology and black hole phenomena.

Abstract

We present a non-perturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts in technical reach applications to cosmology, quantum gravitational collapse and Hawking radiation.