Light from Reissner-Nordstrom-de Sitter black holes

The light from the Reissner-Nordstrom black hole in de Sitter expanding universe is studied deriving for the first time the form of the spiral null geodesics around the photon sphere and the radius of the sphere hosting the apparent sources near the black hole shadow. We obtains thus the principal parameter giving the redshift and the observed black hole shadow according to our method we proposed recently giving its complete calculations and results in an algebraic code on computer [Comp].