  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.
