# Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri's equation

## TL;DR

This paper explores the geodesic deviation and Raychaudhuri's equation within Bohmian quantum mechanics, providing insights into quantum effects on spacetime trajectories without considering back-reaction effects.

## Contribution

It clarifies the application of geodesic deviation and Raychaudhuri's equation in Bohmian quantum mechanics, a framework where trajectories are well-defined, unlike in standard quantum mechanics.

## Key findings

- Analysis of geodesic deviation in Bohmian mechanics
- Insights into quantum effects on gravitational singularities
- Clarification of classical equations in a quantum context

## Abstract

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since, the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the back-reaction effects of matter on the spacetime metric.