New form of all black holes of type D with a cosmological constant

TL;DR

This paper introduces a simplified, explicit metric form for the complete family of algebraic type D black hole spacetimes with a cosmological constant, enabling detailed analysis of their physical and geometrical properties.

Contribution

The authors present a new, more explicit and partially factorized metric form for type D black hole solutions with cosmological constant, clarifying their structure and relationships to known solutions.

Findings

Unified metric form for various black hole solutions

Clarification of the absence of accelerating NUT black holes without rotation

Analysis of horizons, singularities, and thermodynamic properties

Abstract

We present an improved metric form of the complete family of exact black hole spacetimes of algebraic type D, including any cosmological constant. This class was found by Debever in 1971, Plebanski and Demianski in 1976, and conveniently reformulated by Griffiths and Podolsky in 2005. In our new form of this metric the key functions are simplified, partially factorized, and fully explicit. They depend on seven parameters with direct physical meanings, namely m, a, l, alpha, e, g, Lambda which characterize mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges of the black hole, and the cosmological constant, respectively. Moreover, this general metric reduces directly to the familiar forms of (possibly accelerating) Kerr-Newman-(anti-)de Sitter spacetime, charged Taub-NUT-(anti-)de Sitter solution, or (possibly rotating and charged) C-metric with a cosmological constant by simply setting the corresponding parameters to zero. In addition, it shows that the Plebanski-Demianski family does not involve accelerating NUT black holes without the Kerr-like rotation. The new improved metric also enables us to study various physical and geometrical properties, namely the character of singularities, two black-hole and two cosmo-acceleration horizons (in a generic situation), the related ergoregions, global structure including the Penrose conformal diagrams, parameters of cosmic strings causing the acceleration of the black holes, their rotation, pathological regions with closed timelike curves, or thermodynamic quantities.