Rotating Relativistic Thin Disks

TL;DR

This paper constructs models of rotating relativistic disks using Taub-NUT and Kerr metrics, revealing relationships between sound velocity and geodesic velocities, and analyzing stability and heat flow zones.

Contribution

It introduces two new families of rotating relativistic disk models based on well-known metrics, exploring their physical properties and stability characteristics.

Findings

Sound velocity equals geometric mean of geodesic velocities.

Disks can have zones with heat flow.

Boundaries of heat flow zones are unstable to radial perturbations.

Abstract

Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric metric the "sound velocity", $(pressure/density)^{1/2}$, is equal to the geometric mean of the prograde and retrograde geodesic circular velocities of test particles moving on the disk. We also found that for generic disks we can have zones with heat flow. For the two families of models studied the boundaries that separate the zones with and without heat flow are not stable against radial perturbations (ring formation).