New improved form of black holes of type D

TL;DR

This paper introduces a simplified, explicit metric form for the entire family of type D black hole spacetimes, enhancing understanding of their horizons, singularities, and physical properties without complex transformations.

Contribution

The authors derive a new, simplified metric for type D black holes that explicitly depends on six parameters and unifies various known solutions.

Findings

Clear identification of all four horizons

Simplified analysis of extremal and degenerate cases

Explicit dependence on physically meaningful parameters

Abstract

We derive a new metric form of the complete family of black hole spacetimes (without a cosmological constant) presented by Plebanski and Demianski in 1976. It further improves the convenient representation of this large family of exact black holes found in 2005 by Griffiths and Podolsky. The main advantage of the new metric is that the key functions are considerably simplified, fully explicit, and factorized. All four horizons are thus clearly identified, and degenerate cases with extreme horizons can easily be discussed. Moreover, the new metric depends only on six parameters with direct geometrical and physical meaning, namely m, a, l, alpha, e, g which characterize mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges of the black hole, respectively. This general metric reduces directly to the familiar forms of either (possibly accelerating) Kerr-Newman, charged Taub-NUT solution, or (possibly rotating and charged) C-metric by simply setting the corresponding parameters to zero, without the need of any further transformations. In addition, it shows that the Plebanski-Demianski family does not involve accelerating black holes with just the NUT parameter, which were discovered by Chng, Mann and Stelea in 2006. It also enables us to investigate various physical properties, such as the character of singularities, horizons, ergoregions, global conformal structure including the Penrose diagrams, cosmic strings causing the acceleration of the black holes, their rotation, pathological regions with closed timelike curves, or explicit thermodynamic properties. It thus seems that our new metric is a useful representation of this important family of black hole spacetimes of algebraic type D in the asymptotically flat settings.