Arbitrarily deformed Kerr-Newman black hole in an external gravitational field

An exact axisymmetric solution of the Einstein-Maxwell equations possessing two infinite sets of arbitrary real parameters and able to describe a deformed Kerr-Newman black hole in an external gravitational field is presented in a concise analytic form. The validity of Smarr's mass formula is demonstrated for a Kerr-Newman black hole surrounded by an external static gravitational field.