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We compute analytically differential invariants for accelerating, rotatingand charged black holes with a cosmological constant $\Lambda$. In particular,we compute in closed form novel explicit algebraic expressions for curvatureinvariants constructed from covariant derivatives of the Riemann and Weyltensors, such as the Karlhede and the Abdelqader-Lake invariants, for theKerr-Newman-(anti-)de Sitter and accelerating Kerr-Newman-(anti-)de Sitterblack hole spacetimes. We explicitly show that some of the computed curvatureinvariants are vanishing at the event and Cauchy horizons or the ergosurface ofthe accelerating, charged and rotating black holes with a non-zero cosmologicalconstant. Using a particular generalised null-tetrad and the Bianchi identitieswe compute in the Newman-Penrose formalism in closed-analytic form thePage-Shoom curvature invariant for the accelerating Kerr-Newman black hole in(anti-)de Sitter spacetime and prove that is vanishing at the black hole eventand Cauchy horizon radii. Therefore such invariants can serve as possibledetectors of the event horizon and ergosurface for such black hole metricswhich belong to the most general type D solution of the Einstein-Maxwellequations with a cosmological constant. Also the norms associated with thegradients of the first two Weyl invariants in the Zakhary-McIntoshclassification, were studied in detail. Although both locally single out thehorizons, their global behaviour is also intriguing. Both reflect thebackground angular momentum and electric charge as the volume of space allowinga timelike gradient decreases with increasing angular momentum and charge.

Differential curvature invariants and event horizon detection for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime