Non-expanding Plebanski-Demianski space-times

TL;DR

This paper characterizes the complete family of non-expanding Plebanski-Demianski type D space-times, providing explicit solutions, analyzing their structure, and interpreting their physical meaning, including generalizations of classic B-metrics.

Contribution

It explicitly derives the most general form of non-expanding Plebanski-Demianski solutions with cosmological constant and explores their geometric and physical properties.

Findings

Provides explicit metric forms for these space-times

Analyzes their global structure and singularities

Shows they generalize classic B-metrics, including BI and AI-metrics

Abstract

The aim of this work is to describe the complete family of non-expanding Plebanski-Demianski type D space-times and to present their possible interpretation. We explicitly express the most general form of such (electro)vacuum solutions with any cosmological constant, and we investigate the geometrical and physical meaning of the seven parameters they contain. We present various metric forms, and by analyzing the corresponding coordinates in the weak-field limit we elucidate the global structure of these space-times, such as the character of possible singularities. We also demonstrate that members of this family can be understood as generalizations of classic B-metrics. In particular, the BI-metric represents an external gravitational field of a tachyonic (superluminal) source, complementary to the AI-metric which is the well-known Schwarzschild solution for exact gravitational field of a static (standing) source.