On the Einstein Tensor Field Equation and the Newman-Penrose Spinor Field Equations

Since the publication of the Newman-Penrose ("NP") equations in 1962 they have been regarded as simply a di fferent version of the Einstein field equations ("EFEs"). This paper reports the fact that symmetry methods can be employed to reduce the complexity of the NP equations, reformulated in terms of the elements of the metric tensor rather than the spin coe fficients, and to derive the exact solution in the reference frame of an observer who is in radial free fall through the external vacuum gravitational field of an isolated, non-rotating, spherically symmetric gravitating body. While the domain of the solution is confined to the axis along which the observer falls, it can be directly compared to the Schwarzschild solution and is shown to di ffer from that solution.