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

We compute analytically differential invariants for accelerating, rotating and charged black holes with a cosmological constant $\Lambda$. In particular, we compute in closed form novel explicit algebraic expressions for curvature invariants constructed from covariant derivatives of the Riemann and Weyl tensors, such as the Karlhede and the Lake-Abdelqader invariants, for the Kerr-Newman-(anti-)de Sitter and accelerating Kerr-Newman-(anti-)de Sitter black hole spacetimes. We explicitly show that some of the computed curvature invariants are vanishing on the event and Cauchy horizons and/or the ergosurface of the accelerating, charged and rotating black holes with a non-zero cosmological constant. Therefore they can serve as possible detectors of the event horizon and ergosurface for such black hole metrics which belong to the most general type D solution of the Einstein-Maxwell equations with a cosmological constant.