Revisiting black holes of algebraic type D with a cosmological constant

TL;DR

This paper comprehensively analyzes a family of algebraic type D black hole solutions with various physical parameters and cosmological constant, unifying different metric forms and focusing on accelerating NUT black holes without rotation.

Contribution

It demonstrates the local equivalence of multiple metric representations of type D solutions and characterizes the full parameter space of these black holes with cosmological constant.

Findings

Unified various metric forms of type D black holes

Established local equivalence of different solution representations

Characterized the parameter space of accelerating NUT black holes

Abstract

As an extension of our previous work [1] (arXiv:2409.02308), we study a complete family of type D black holes with Kerr-like rotation, NUT twist, acceleration, electric and magnetic charges, and any value of the cosmological constant $\Lambda$. We relate various metric forms of these spacetimes, namely those found by Plebanski-Demianski (PD), Griffiths-Podolsky (GP), and most recently Astorino (A). By explicit coordinate transformations and proper identification of the physical parameters we show that these representations are locally equivalent, and cover the entire class of type D solutions of the Einstein-Maxwell-$\Lambda$ equations, such that the (non-null) electromagnetic field is aligned with both the (double-degenerate) principal null directions of the Weyl tensor. In particular, we concentrate on the subclass which describes accelerating NUT black holes without the Kerr-like rotation.