Spacetime symmetries and geometric diffusion

Abstract

We examine relativistic diffusion through the frame and observer bundles associated with a Lorentzian manifold $(M,g)$. Our focus is on spacetimes with a non-trivial isometry group, and we detail the conditions required to find symmetric solutions of the relativistic diffusion equation. Additionally, we analyze the conservation laws associated with the presence of Killing vector fields on $(M,g)$ and their implications for the expressions of the geodesic spray and the vertical Laplacian on both the frame and the observer bundles. Finally, we present several relevant examples of symmetric spacetimes.

29 pages. Accepted for publication in Journal of Physics A: Mathematical and Theoretical

References in corpus (12)

• Relativistic Brownian Motion
• The geometry of the tangent bundle and the relativistic kinetic theory of gases
• A simple proof of Birkhoff's theorem for cosmological constant
• Cosmology with matter diffusion
• A kinetic theory of diffusion in general relativity with cosmological scalar field
• An introduction to the relativistic kinetic theory on curved spacetimes
• Relativistic Kinetic Theory: An Introduction
• Cosmological models with fluid matter undergoing velocity diffusion
• Finsler-Randers-Sasaki gravity and cosmology
• Dynamics of Robertson-Walker spacetimes with diffusion
• Thermodynamics of diffusive DM/DE systems
• Brownian motion at the speed of light: a Lorentz invariant family of processes