  The Pleba\'{n}ski--Demia\'{n}ski solution is a very general axially symmetric
analytical solution of the Einstein field equations generalizing the Kerr
solution. This solution depends on seven parameters which under certain
circumstances are related to mass, rotation, cosmological constant, NUT
parameter, electric and magnetic charges, and acceleration. In this paper we
present a general description of matter wave interferometry in the general
Pleba\'{n}ski--Demia\'{n}ski black hole space--time. Particular emphasis is
placed on a gauge invariant description of the symmetries of the gauge field.
We show that it is possible to have access to all parameters separately except
the acceleration. For neutral particles there is only access to a combination
of electric and magnetic charge.
