A solution of the Weyl-Lanczos equations for the Schwarzschild space-time (Q1878371)

The Lanczos tensor \(H_{abc}\) can be obtained from the curvature tensor (Weyl conformal tensor) on every four dimensional (pseudo-) Riemannian manifold. It has been established that \(H_{abc}\) corresponds to a four-valent spinor \(H_{ABCC^\prime}\), called the Lanczos spinor. Then \(8\) Lanczos coefficients can be obtained from this spinor. A spinor \(H_{ABCC^\prime}\) on the manifold \(M\) is a Lanczos spinor if and only if the Weyl-Lanczos equations are fulfilled. The author studies the spin coefficient form of the Weyl-Lanczos equations for the Schwarzschild space-time. This investigation has given rise to a new solution by introducing a new technique.