# Disk sources of the Kerr and Tomimatsu-Sato spacetimes: construction and physical properties

## TL;DR

This paper constructs and analyzes disk sources for Kerr and Tomimatsu-Sato spacetimes, exploring matter models, rotational effects, and physical constraints to understand their properties and limitations.

## Contribution

It introduces models of disk sources for these spacetimes, demonstrating their generality and limitations, especially regarding rotation, pressure, and compactness.

## Key findings

- Rotating rings model describes all axisymmetric stationary disk sources with vanishing radial pressure.
- Centrifugal effects limit the compactness of disks formed by counter-rotating geodesic streams.
- Dragging effects induce rotation or asymmetry in the disk matter distributions.

## Abstract

We construct the disk sources matched to the exact vacuum Kerr and to the two classes of Tomimatsu-Sato spacetimes. We analyze two models of the matter forming these disks. At each radius we consider either a rotating massive ring with pressure or two counter-rotating streams of particles in circular geodesic motion. Dragging effects present in such spacetimes lead either to rotation of rings or asymmetry of both streams. We demonstrate that the model of rotating rings is general enough to describe all axisymmetric stationary disk sources with vanishing radial pressure which satisfy weak energy condition, and that centrifugal effects present in the disk sources of spacetimes with large angular momentum prevent the construction of highly compact sources made of counter-rotating streams of geodesic particles. We illustrate the radial distribution of the mass inside the disks and the angular velocities of both geodesic streams.