Stationary axisymmetric systems that allow for a separability structure

TL;DR

This paper presents a systematic framework for identifying and constructing stationary, axisymmetric spacetimes with matter fields that admit separability, leading to new solutions like rotating black holes with monopoles and wormholes.

Contribution

It introduces a general metric ansatz for separability in matter-supported stationary axisymmetric spacetimes and constructs new explicit solutions demonstrating this framework.

Findings

Derived a broad family of separable rotating solutions.

Constructed a rotating black hole with a monopole.

Developed a new class of rotating wormhole geometries.

Abstract

We develop a systematic framework for formulating and solving the conditions that lead to separability in stationary, axisymmetric spacetimes in the presence of matter fields. Guided by Carter's metric form, we introduce a general stationary, axisymmetric metric ansatz that allows for a transparent separation of radial and angular variables. This construction yields a broad family of stationary rotating solutions admitting separability structures. To illustrate the applicability of the formalism, we explicitly construct several examples, including a rotating black hole with a global monopole supported by anisotropic matter, as well as a new class of rotating wormhole geometries.