  This paper explores the Kerr-Schild double copy, a duality relating gravity
and electromagnetism. We show how Einstein's vacuum solutions in four
dimensions can be converted into Maxwell's solutions via a double copy
procedure, employing tensor fields. This technique yields novel solutions to
Einstein's equations, including Kerr, Schwarzschild, and RN black holes.
Introduced by Kerr and Schild in 1965, the Kerr-Schild action decouples the
gravitational and matter fields, surpassing the Einstein-Hilbert action in
facilitating calculations. It holds significant value for studying
gravitational waves, cosmology, and black hole thermodynamics. We further delve
into the applications of the Kerr-Schild double copy in deriving black hole
solutions, analyzing gravitational waves, exploring alternative cosmological
theories, and understanding black hole thermodynamics. Moreover, we investigate
the implications of this double copy under SO(3) and SU(2) symmetries on the
Schwarzschild and Kerr-Newman black hole metrics.
