Exact Relativistic Gravitational Field of a Stationary Counterrotating Dust Disk

TL;DR

This paper derives an exact solution to Einstein's equations for a thin, stationary, axisymmetric dust disk composed of two counterrotating streams, unifying several known models and exploring relativistic effects.

Contribution

It presents a new exact solution for a counterrotating dust disk in general relativity, connecting and generalizing previous models like the Neugebauer-Meinel and Morgan-Morgan disks.

Findings

Solution includes ergospheres in certain regimes

Unifies static and rigidly rotating disk models

Analyzes Newtonian and ultrarelativistic limits

Abstract

Disks of collisionless particles are important models for certain galaxies and accretion disks in astrophysics. We present here a solution to the stationary axisymmetric Einstein equations which represents an infinitesimally thin dust disk consisting of two streams of particles circulating with constant angular velocity in opposite directions. These streams have the same density distribution but their relative density may vary continuously. In the limit of only one component of dust, we get the solution for the rigidly rotating dust disk previously given by Neugebauer and Meinel, in the limit of identical densities, the static disk of Morgan and Morgan is obtained. We discuss the Newtonian and the ultrarelativistic limit, the occurrence of ergospheres, and the regularity of the solution.