Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes
  as gravitational lenses
  The null geodesic equations that describe motion of photons in Kerr spacetime
are solved exactly in the presence of the cosmological constant $\Lambda$. The
exact solution for the deflection angle for generic light orbits (i.e.
non-polar, non-equatorial) is calculated in terms of the generalized
hypergeometric functions of Appell and Lauricella. We then consider the more
involved issue in which the black hole acts as a `gravitational lens'. The
constructed Kerr black hole gravitational lens geometry consists of an observer
and a source located far away and placed at arbitrary inclination with respect
to the black hole's equatorial plane. The resulting lens equations are solved
elegantly in terms of Appell-Lauricella hypergeometric functions and the
Weierstrass elliptic function. We then, systematically, apply our closed form
solutions for calculating the image and source positions of generic photon
orbits that solve the lens equations and reach an observer located at various
values of the polar angle for various values of the Kerr parameter and the
first integrals of motion. In this framework, the magnification factors for
generic orbits are calculated in closed analytic form for the first time. The
exercise is repeated with the appropriate modifications for the case of a
non-zero cosmological constant.
