Hot, Rotating Disks In General Relativity: Collisionless Equilibrium Models

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. 1. INTRODUCTION Rotating stellar disks in dynamical equilibrium have a long history in astrophysics. Such systems are described by self-consistent solutions to the Vlasov equation for the phase-space distribution function f coupled to the equations for the gravitational field. Even in Newtonian gravitation, finding..