Kerr–Schild Tetrads and the Nijenhuis Tensor

We write the Kerr–Schild tetrads in terms of flat space–time and a (1, 1) tensor Sμλ. This can be considered as projection operator, since it transforms (i) into non-flat tetrads, vice-versa, (ii) Minkowski metric tensor, vice-versa. The Sμλ its inverse are constructed standard null vector field lμ that defines form general relativity, yields black holes non-linear gravitational waves solutions vacuum Einstein’s equations. demonstrate condition for vanishing Ricci obtained by Kerr Schild, empty space–time, is also Nijenhuis out Thus, theory based on an important class equations, namely, waves. present mathematical framework easily admit modifications Newtonian potential may explain long range effects related to galaxy rotation curves.