https://doi.org/10.1140/epjp/i2017-11393-0
Regular Article
Separation of arbitrary spin wave equations in a class of 
LTB cosmologies
Wave equations in LTB cosmology
1
Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, 20133, Milano, Italy
2
GNFM, Gruppo Nazionale per la Fisica Matematica, Milano, Italy
* e-mail: antonio.zecca@mi.infn.it
Received:
12
December
2016
Accepted:
2
February
2017
Published online:
2
March
2017
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017
