Relativistic kinetic gases as direct sources of 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.

arXiv comment13 pages, updated to journal version

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• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Cosmological Finsler Spacetimes
• Mathematical foundations for field theories on Finsler spacetimes
• Foundations of Finsler spacetimes from the Observers' Viewpoint
• Schwarzschild-like solutions in Finsler-Randers gravity
• Canonical variational completion and 4D Gauss-Bonnet gravity
• The kinetic gas universe
• Jupiter and jovian (exo)-planets in Palatini $f(\bar{R})$ gravity
• Randers pp-waves
• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• General Teleparallel Modifications of Schwarzschild Geometry
• Identifying Berwald Finsler Geometries
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• A Cosmological Unicorn Solution to Finsler Gravity
• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Relativistic deformed kinematics: from flat to curved spacetimes
• The Finsler spacetime condition for (α,β)-metrics and their isometries
• Cosmological Landsberg Finsler spacetimes
• On the significance of the stress-energy tensor in Finsler spacetimes
• Multimetric Finsler Geometry
• Weak equivalence principle and nonrelativistic limit of general dispersion relations
• Birkhoff Theorem for Berwald Finsler spacetimes
• Metrizability of SO(3)-invariant connections: Riemann versus Finsler
• From kinetic gases to an exponentially expanding universe - The Finsler-Friedmann equation
• Kinetic gases in static spherically symmetric modified dispersion relations