Gravitational lensing and frame dragging of light in the Kerr-Newman and
  the Kerr-Newman-(anti) de Sitter black hole spacetimes
  The null geodesics that describe photon orbits in the spacetime of a rotating
electrically charged black hole (Kerr-Newman) are solved exactly including the
contribution from the cosmological constant. We derive elegant closed form
solutions for relativistic observables such as the deflection angle and frame
dragging effect that a light ray experiences in the gravitational fields (i) of
a Kerr-Newman black hole and (ii) of a Kerr-Newman-de Sitter black hole. We
then solve the more involved problem of treating a Kerr-Newman black hole as a
gravitational lens, i.e. a KN black hole along with a static source of light
and a static observer both located far away but otherwise at arbitrary
positions in space. For this model, we derive the analytic solutions of the
lens equations in terms of Appell and Lauricella hypergeometric functions and
the Weierstra\ss modular form. The exact solutions derived for null, spherical
polar and non-polar orbits, are applied for the calculation of frame dragging
for the orbit of a photon around the galactic centre, assuming that the latter
is a Kerr-Newman black hole. We also apply the exact solution for the
deflection angle of an equatorial light ray in the gravitational field of a
Kerr-Newman black hole for the calculation of bending of light from the
gravitational field of the galactic centre for various values of the Kerr
parameter, electric charge and impact factor. In addition, we derive analytic
expressions for the Maxwell tensor components for a
Zero-Angular-Momentum-Observer (ZAMO) in the Kerr-Newman-de Sitter spacetime.
