Classical and quantum analysis of gravitational singularity from Raychaudhuri equation

TL;DR

This paper investigates gravitational singularities using the Raychaudhuri equation from both classical and quantum perspectives, exploring their effects on black holes and the big bang, and proposing quantum resolutions.

Contribution

It introduces a novel analysis of the Raychaudhuri equation through classical harmonic oscillator models and quantum approaches including canonical quantization and Bohmian trajectories.

Findings

Raychaudhuri scalar influences singularity formation

Quantum methods suggest possible resolution of big-bang singularity

Classical analysis links Raychaudhuri equation to harmonic oscillator dynamics

Abstract

The present work deals with the Raychaudhuri equation (RE) to examine the space-time singularity both from classical and quantum point of view. The RE has been looked upon in terms of a classical linear Harmonic oscillator and Focusing theorem has been studied. Also, the Raychaudhuri scalar has been shown to affect the convergence and singularity formation in Black-holes and cosmology. Finally, resolution of initial big-bang singularity has been attempted quantum mechanically in two ways namely by canonical quantization and by formulation of Bohmian trajectories.