Weyl Spinor and Solution of Massless Free Field Equations

The massless field equations for arbitrary spin in curved space-time arereconsidered. The general solution of the field equation in Robertson-Walkerspace-time that was previously determined is briefly discussed after explicitlyshowing that the Weyl spinor vanishes. The case of the Lemaître-Tolman-Bondispace-time is studied in detail. The general expression of the corresponding Weylspinor is obtained and some particular situations exploited. The spin-3/2 andspin-2 massless field equations are solved explicitly. The solutions are simplifiedby the existence of nontrivial algebraic constraints. The angular part of theequations is separated by the usual separation method and integrated directly.The other equations that are not separated in the radial and time dependence arereduced to a simple form. The results obtained are extended, as a consequenceof previous results, to the case of arbitrary spin. The solution of the general caseessentially reduces to the treatment of spin 3/2 and spin 2.