A vortex model for rotating compact objects

TL;DR

This paper introduces a new vortex model for rotating compact objects in general relativity, revealing a phase transition and vortex structure that differ from traditional Kerr solutions, with implications for understanding their internal geometry.

Contribution

It presents a novel rotating vacuum solution with a vortex structure, connecting de Sitter space to a new phase of space-time near the axis of rotation.

Findings

A vortex structure appears near the axis of rotation.

The solution reduces to de Sitter space when angular momentum is zero.

Deviations from Kerr are significant at polar latitudes.

Abstract

A rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter's interior cosmological solution when the angular momentum goes to zero. This solution is locally isomorphic to de Sitter space, but as one approaches the axis of rotation a conical event horizon appears that signals the appearance of a new phase of space-time. This suggests that in reality rotating compact objects have a vortex structure similar to that conjectured for rotating superfluid droplets. In the limit of slow rotation the vortex core would be nearly cylindrical and the space-time inside the core would be Godel-like. The exterior space-time will resemble the Kerr solution for equatorial latitudes, but significant deviations from Kerr are expected for polar latitudes.