A new look at the Plebanski-Demianski family of solutions

TL;DR

This paper revisits the Plebanski-Demianski family of solutions, providing a new form of the metric that clarifies physical interpretation and subfamily classification, including parameters for acceleration and twist.

Contribution

Introduces a new form of the Plebanski-Demianski metric that simplifies analysis and highlights physical parameters such as acceleration and twist.

Findings

Explicit inclusion of acceleration and twist parameters in the metric

Clear identification of expanding and non-expanding solutions

Simplified derivation of special cases

Abstract

The Plebanski-Demianski metric, and those that can be obtained from it by taking coordinate transformations in certain limits, include the complete family of space-times of type D with an aligned electromagnetic field and a possibly non-zero cosmological constant. Starting with a new form of the line element which is better suited both for physical interpretation and for identifying different subfamilies, we review this entire family of solutions. Our metric for the expanding case explicitly includes two parameters which represent the acceleration of the sources and the twist of the repeated principal null congruences, the twist being directly related to both the angular velocity of the sources and their NUT-like properties. The non-expanding type D solutions are also identified. All special cases are derived in a simple and transparent way.