# The Bakry-\'Emery Ricci tensor: Application to mass distribution in space-time

## TL;DR

This paper introduces a modified Einstein field equation incorporating the Bakry-Émery Ricci tensor, linking mass distribution directly to geometric properties of space-time.

## Contribution

It proposes a novel geometric framework that integrates mass into the fabric of space-time using the Bakry-Émery Ricci tensor, extending classical general relativity.

## Key findings

- New Einstein field equation with Bakry-Émery Ricci tensor
- Mass distribution modeled as geometric property
- Potential implications for understanding dark matter

## Abstract

The notion of Barky-Emery Ricci tensor motivates new version of Einstein field equation in which mass becomes part of geometry.