Relativistic kinetic gases as direct sources of gravity

TL;DR

This paper introduces a Finsler geometric framework for modeling the gravitational field generated by a kinetic gas, extending general relativity to tangent bundle geometry and ensuring energy-momentum conservation.

Contribution

It develops a novel coupling between kinetic gases and Finsler geometry, providing a new approach to gravitating multi-particle systems.

Findings

Constructed a Finsler spacetime model for kinetic gases.

Derived a conservation law for energy-momentum on the tangent bundle.

Linked kinetic gas properties to Finsler geometric gravity.

Abstract

We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e. on the tangent bundle of the spacetime manifold. We argue that an appropriate theory of gravity, describing the gravitational field generated by a kinetic gas, must also be modeled on the tangent bundle. The most natural mathematical framework for this task is Finsler spacetime geometry. Following this line of argumentation, we construct a coupling between the kinetic gas and a recently proposed Finsler geometric extension of general relativity. Additionally, we explicitly show how the coordinate invariance of the action of the kinetic gas leads to a novel formulation of conservation of the energy-momentum distribution of the gas on the tangent bundle.