Various metric forms of all type D black holes and their application

TL;DR

This paper summarizes various exact solutions of type D black holes in Einstein-Maxwell-$\Lambda$ equations, exploring their metrics, properties, and the link between acceleration and gravitational radiation.

Contribution

It presents new metric representations and analyzes the physical and geometrical properties of a broad class of charged, rotating, and accelerating black holes.

Findings

Type D black holes with acceleration emit gravitational radiation.

Different metric forms are related and useful for studying horizons and singularities.

Acceleration is directly linked to gravitational wave emission.

Abstract

Several recent results concerning the complete class of exact solutions to the Einstein-Maxwell-$\Lambda$ equations of type D with a double-aligned electromagnetic field are summarized. This large class of spacetimes includes charged black holes with rotation, NUT parameter, and acceleration. In particular, we present their Plebanski-Demianski, Griffiths-Podolsky-Vratny, and Astorino metric representations, we discuss mutual relations between them, and demonstrate their usefulness for investigation of physical and geometrical properties (singularities, horizons, conformal diagrams, ergoregions, rotating strings causing the acceleration, thermodynamics). It includes the proof that such black holes emit gravitational radiation if, and only if, they accelerate. Very recent extension to type D black holes with non-aligned Maxwell field is also mentioned.