Refined Perspectives on the Kerr-Schild Double Copy:Harmonizing Gravity and Electromagnetism in Metric Formulations

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.