Hot, Rotating Disks In General Relativity: Collisionless Equilibrium Models

TL;DR

This paper introduces a novel method for constructing equilibrium, rotating disk models in general relativity by solving the coupled relativistic Vlasov and Einstein equations, extending Newtonian disk solutions into the relativistic regime.

Contribution

It presents the first relativistic, rotating collisionless disk solutions by coupling the Vlasov equation with Einstein's equations, generalizing Newtonian models.

Findings

Constructed relativistic disk models with angular momentum.

Analyzed stability against ring formation.

Explored relativistic equilibrium sequences for various velocity dispersions.

Abstract

We present a method for constructing equilibrium disks with net angular momentum in general relativity. The method solves the relativistic Vlasov equation coupled to Einstein's equations for the gravitational field. We apply the method to construct disks that are relativistic versions of Newtonian Kalnajs disks. In Newtonian gravity these disks are analytic, and are stable against ring formation for certain ranges of their velocity dispersion. We investigate the existence of fully general relativistic equilibrium sequences for differing values of the velocity dispersion. These models are the first rotating, relativistic disk solutions of the collisionless Boltzman equation.