Exact General Relativistic Perfect Fluid Disks with Halos

TL;DR

This paper constructs static, relativistic perfect fluid disks with halos using a method applied to Einstein's equations solutions, analyzing their physical properties and stability.

Contribution

It introduces a new class of exact solutions for relativistic disks with halos derived from known Einstein solutions, exploring their physical characteristics.

Findings

Disks exhibit decreasing surface energy density and pressure with radius.

Higher relativistic disks have more concentrated energy and pressure near the center.

Disks can be modeled with subluminal sound and tangential velocities.

Abstract

Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic coordinates. The same method is applied to different exactsolutions to the Einstein'sequations that represent static spheres of perfect fluids. We construct several models of disks with axially symmetric perfect fluid halos. All disks have some common features: surface energy density and pressures decrease monotonically and rapidly with radius. As the ``cut'' parameter $a$ decreases, the disks become more relativistic, with surface energy density and pressure more concentrated near the center. Also regions of unstable circular orbits are more likely to appear for high relativistic disks. Parameters can be chosen so that the sound velocity in the fluid and the tangential velocity of test particles in circular motion are less then the velocity of light. This tangential velocity first increases with radius and reaches a maximum.