# Nonlinear diffusion in relativistic kinetic theory

## TL;DR

This paper introduces a Lorentz invariant nonlinear kinetic diffusion equation compatible with conservation laws, which converges to Maxwellian in the Newtonian limit and can be integrated with Einstein's equations.

## Contribution

It presents a novel nonlinear diffusion model in relativistic kinetic theory that differs from the traditional Jüttner distribution and is compatible with general relativity.

## Key findings

- Equilibrium solution converges to Maxwellian density in the Newtonian limit.
- Equation is consistent with conservation laws and Einstein's equations.
- Not based on the Jüttner distribution.

## Abstract

A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian limit, but it is not given by the J\"uttner distribution commonly employed in relativistic kinetic theory. The nonlinear kinetic diffusion equation on a general Lorentzian manifold is consistent with the contracted Bianchi identities and therefore can be coupled to the Einstein equations of general relativity.