A new class of anisotropic rotating fluids and some throat-like sources for Kerr metric as examples

TL;DR

This paper introduces a new class of anisotropic rotating solutions that serve as potential sources for the Kerr metric, enabling the modeling of regular black holes, wormholes, and galactic structures with dark matter halos.

Contribution

It presents novel anisotropic rotating solutions compatible with the Kerr metric, including traversable wormholes and throat geometries, satisfying all energy conditions.

Findings

A 5-parameter class of traversable wormhole solutions.

Solutions satisfy all energy conditions outside the wormhole.

Modified solutions provide Kerr sources with throat geometries.

Abstract

Motivated by the increasing interest in finding physically viable rotating sources, we present a new class of anisotropic rotating solutions. The energy-momentum tensor compatible with the metric is composed of anisotropic matter with a non-vanishing energy flow around the symmetry axis and vanishing viscosity. The new class of solutions can be used to find new possible sources for the Kerr metric, to obtain new regular black hole solutions and to study galaxies with a central rotating black hole and an halo of dark matter. As an example, we obtain a 5-parameter class of solutions representing a two-way traversable wormhole smoothly matched to the Kerr one and satisfying all energy conditions outside the wormhole for a wide range of parameters, in particular for compact objects. Finally, with a simple modification of the aforementioned solution, we obtain a source for Kerr metric with a throat geometry, non-representing a two-way traversable wormhole and satisfying all energy conditions.