Gravitational redshift/blueshift of light emitted by geodesic test
  particles, frame-dragging and pericentre-shift effects, in the Kerr-Newman-de
  Sitter and Kerr-Newman black hole geometries
  We investigate the redshift and blueshift of light emitted by timelike
geodesic particles in orbits around a Kerr-Newman-(anti) de Sitter (KN(a)dS)
black hole. Specifically we compute the redshift and blueshift of photons that
are emitted by geodesic massive particles and travel along null geodesics
towards a distant observer-located at a finite distance from the KN(a)dS black
hole. For this purpose we use the Killing-vector formalism and the associated
first integrals-constants of motion. We consider in detail stable timelike
equatorial circular orbits of stars and express their corresponding
redshift/blueshift in terms of the metric physical black hole parameters
(angular momentum per unit mass, mass, electric charge and the cosmological
constant) and the orbital radii of both the emitter star and the distant
observer. These radii are linked through the constants of motion along the null
geodesics followed by the photons since their emission until their detection
and as a result we get closed form analytic expressions for the orbital radius
of the observer in terms of the emitter radius, and the black hole parameters.
In addition, we compute exact analytic expressions for the frame dragging of
timelike spherical orbits in the KN(a)dS spacetime in terms of multivariable
generalised hypergeometric functions of Lauricella and Appell. We solve the
conditions for timelike spherical orbits in KN(a)dS and KN spacetimes. We
present new, elegant compact forms for the parameters of these orbits. Last but
not least we derive a very elegant and novel exact formula for the periapsis
advance for a test particle in a non-spherical polar orbit in KNdS black hole
spacetime in terms of Jacobi's elliptic function sn and Lauricella's
hypergeometric function $F_D$.
