Kinetic gases in static spherically symmetric modified dispersion relations

TL;DR

This paper analyzes the behavior of collisionless kinetic gases under general static, spherically symmetric modified dispersion relations, deriving solutions and exploring implications for quantum gravity phenomenology near compact objects.

Contribution

It derives the most general solutions for kinetic gases with modified dispersion relations in static, spherically symmetric spacetimes, including specific cases like monoenergetic shells and radial inflow.

Findings

Derived general solutions depending on three variables

Calculated particle density profiles for specific solutions

Explored effects of $$-Poincare9 modifications on particle density

Abstract

We study the dynamics of a collisionless kinetic gas in the most general static, spherically symmetric dispersion relation. For a static, spherically symmetric kinetic gas, we derive the most general solution to these dynamics, and find that any solution is given by a one-particle distribution function which depends on three variables. For two particular solutions, describing a shell of monoenergetic orbiting particles and a purely radial inflow, we calculate the particle density as a function of the radial coordinate. As a particular example, we study a $\kappa$-Poincar\'e modification of the Schwarzschild metric dispersion relation and derive its influence on the particle density. Our results provide a possible route towards quantum gravity phenomenology via the observation of matter dynamics in the vicinity of massive compact objects.