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In an earlier paper we have analytically determined the photon regions andthe shadows of black holes of the Pleba\'nski class of metrics which are alsoknown as the Kerr--Newman--NUT--(anti-)deSitter metrics. These metrics arecharacterized by six parameters: mass, spin, electric and magnetic charge,gravitomagnetic NUT charge, and the cosmological constant. Here we extend thisanalysis to the Pleba\'nski--Demia\'nski class of metrics which contains, inaddition to these six parameters, the so-called acceleration parameter. Allthese metrics are axially symmetric and stationary type D solutions to theEinstein--Maxwell equations with a cosmological constant. We derive analyticalformulas for the photon regions (i.e., for the regions that contain sphericallightlike geodesics) and for the boundary curve of the shadow as it is seen byan observer at Boyer--Lindquist coordinates $(r_O, \vartheta _O)$ in the domainof outer communication. Whereas all relevant formulas are derived for the wholePleba\'nski--Demia\'nski class, we concentrate on the accelerated Kerr metric(i.e., only mass, spin and acceleration parameter are different from zero) whendiscussing the influence of the acceleration parameter on the photon region andon the shadow in terms of pictures. The accelerated Kerr metric is also knownas the rotating $C$-metric. We discuss how our analytical formulas can be usedfor calculating the horizontal and vertical angular diameters of the shadow andwe estimate these values for the black holes at the center of our Galaxy and atthe center of M87.

Photon Regions and Shadows of Accelerated Black Holes