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Spin 3/2 Field Equation: Separation and Solution in a Class of Lemaître–Tolman–Bondi Cosmologies

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Abstract

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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Authors and Affiliations

  1. Via Celoria 16, 20133, Milano, Italy

    Antonio Zecca

  2. GNFM—Gruppo Nazionale per la Fisica Matematica, Sesto Fiorentino (Fi), Italy

    Antonio Zecca

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  1. Antonio Zecca
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Correspondence to Antonio Zecca.

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Zecca, A. Spin 3/2 Field Equation: Separation and Solution in a Class of Lemaître–Tolman–Bondi Cosmologies. Int J Theor Phys 51, 438–446 (2012). https://doi.org/10.1007/s10773-011-0920-x

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  • DOI: https://doi.org/10.1007/s10773-011-0920-x

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