Mathematics – Logic
Scientific paper
Feb 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012ijtp...51..438z&link_type=abstract
International Journal of Theoretical Physics, Volume 51, Issue 2, pp.438-446
Mathematics
Logic
Lemaître-Tolman-Bondi Cosmological Model, Spin 3/2 Field Equation, Variable Separation, Solutions
Scientific paper
The spin 3/2 field equation is studied in the general Lemaître-Tolman-Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson-Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.
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