The Wahlquist-Newman solution

TL;DR

This paper introduces the Wahlquist-Newman metric, a new exact solution in general relativity that generalizes the Wahlquist and Kerr-Newman metrics, revealing geometric properties and special cases within a family of solutions.

Contribution

It presents the explicit form of the Wahlquist-Newman metric, a charged generalization of the Wahlquist solution, and explores its geometric properties and special cases.

Findings

The Wahlquist-Newman metric includes Kerr-Newman-de Sitter and Wahlquist as special cases.

It exhibits specific geometric properties related to electromagnetic fields and horizons.

The metric's parameters and limits are thoroughly characterized.

Abstract

Based on a geometrical property which holds both for the Kerr metric and for the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically preferred charged generalization of the Kerr metric. We discuss which geometric property makes this metric so special and claim that a charged generalization of the Wahlquist metric satisfying a similar property should exist. This is the Wahlquist-Newman metric, which we present explicitly in this paper. This family of metrics has eight essential parameters and contains the Kerr-Newman-de Sitter and the Wahlquist metrics, as well as the whole Pleba\'nski limit of the rotating C-metric, as particular cases. We describe the basic geometric properties of the Wahlquist-Newman metric, including the electromagnetic field and its sources, the static limit of the family and the extension of the spacetime across the horizon.