# Quantum no-singularity theorem from geometric flows

## TL;DR

This paper develops a quantum version of geometric flows related to the Raychaudhuri equation, suggesting that quantum effects can prevent classical singularities in spacetime by eliminating conjugate points.

## Contribution

It introduces a quantization of geometric flows based on the Raychaudhuri equation, providing a framework to show quantum space-times are non-singular.

## Key findings

- Quantum geometric flow prevents conjugate points.
- Quantum effects imply a complete, non-singular spacetime.
- Provides a new approach to quantum gravity and singularity resolution.

## Abstract

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (non-singular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.