Black Holes, Gravitational Waves and Quantum Gravity

TL;DR

This paper discusses the potential for combining black holes and gravitational waves within Loop Quantum Gravity, emphasizing the quantization of geometric quantities like area and volume.

Contribution

It introduces foundational ideas for a future rigorous approach to unify black holes and gravitational waves using Loop Quantum Gravity's geometric quantization.

Findings

Quantization of geometric quantities in Loop Quantum Gravity.

Proposed framework for black holes and gravitational waves.

Future directions for rigorous mathematical formulation.

Abstract

Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric quantities such as area and volume are quantized in terms of the Planck lenth. In this paper we present the basic ideas for a future, mathematically more rigorous, attempt to combine black holes and gravitational waves using the quantization of geometric quantities introduced by Loop Quantum Gravity.