Separation of arbitrary spin wave equations in a class of $\Lambda$ Λ LTB cosmologies

Abstract

The arbitrary spin field equations that are not separable, contrarily to what happens in the Robertson-Walker and Schwarzschild metrics, are studied in a general comoving spherically symmetric metric. They result to be separable by variable separation in a class of metrics governing the Lemâitre Tolman Bondi cosmological models whose physical radius has a special factorized parametric representation. The result is proved by induction by explicitly considering the spin 1, 3/2, 2 case and then the higher spin values. The procedure is based on the Newman-Penrose formalism, which takes into account the strong analogy with the Robertson-Walker metric case. The existence of a nontrivial Weyl spinor requires a symmetrization of one of the spinor wave equations for spin values greater than 1.