Abstract
The problem of variable separation of the scalar field equation is approached within the Lemaître-Tolman-Bondi (LTB) cosmological model with cosmological constant Λ. Parametric solutions of the cosmological Newton-like equation of the model are preliminary determined that result factorized in the parameter and in the radial dependence. The result holds on a sufficient condition that relates the two arbitrary integration functions of the model. The condition is of the same type of the one that ensures, in absence of cosmological term, the separability of the spin field equations for spin 0, 1/2, 1. It is then shown that the scalar field equation results automatically separable in the class of LTB models determined. The separated radial equation results independent of Λ, while the separated time equation strictly depends on Λ. The separability of the field equations is then checked to hold, in the same context, for spinor field equation of spin 1/2 and spin 1.
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References
Lemaître, G.: The expanding universe. Gen. Relativ. Gravit. 29, 641–680 (1997)
Tolman, R.C.: Effect of inhomogeneity on cosmological models. Proc. Natl. Acad. Sci. USA 20, 169–176 (1934)
Bondi, H.: Spherically symmetric models in general relativity. Mon. Not. R. Astron. Soc. 107, 410–425 (1947)
Krasinski, A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1997)
Zecca, A.: On the Tolman-Bondi model with cosmological term. Nuovo Cimento 106 B, 413–418 (1991)
Romano, E.A., Chen, P.: Analytical estimation of the corrections to the apparent value of the cosmological constant due to large scale structure (2012). arXiv:1207.5572v2 [astro-ph.CO]
Demianski, M., Lasota, J.P.: Black holes in an expanding universe. Nat. Phys. Sci. 241, 53–55 (1973)
Zecca, A.: Collapse and singularities in Lemaître-Tolman-Bondi models. Nuovo Cimento 116 B, 1195–1202 (2001)
Zecca, A.: Dirac equation in Lemaître-Tolman-Bondi cosmological model. Gen. Relativ. Gravit. 32, 1197–1206 (2000)
Zecca, A.: Scalar field equation in Lemaître-Tolman-Bondi cosmological model. Nuovo Cimento 116 B, 341–350 (2001)
Zecca, A.: Separation and solution of spin 1 field equation and particle production in Lemaître-Tolman-Bondi cosmologies. In: Alfonso-Faus, A. (ed.) Aspects of Today Cosmology. Intech, Rijeka (2011)
Newman, E., Penrose, R.: An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys. 3, 566–578 (1962)
Illge, R.: Massive fields of arbitrary spin in curved spacetimes. Commun. Math. Phys. 158, 433–457 (1993)
Zecca, A.: Weyl spinor and solutions of massless free field equations. Int. J. Theor. Phys. 39, 377–387 (2000)
Zecca, A.: Separation of massive field equation of arbitrary spin in Robertson-Walker space-time. Nuovo Cimento 121 B, 167–173 (2006)
Zecca, A.: Spinor field equation of arbitrary spin in Robertson-Walker space-time: solution. Adv. Stud. Theor. Phys. 4, 353–362 (2010)
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)
Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982)
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Zecca, A. Separation of Spin 0, 1/2, 1 Field Equations in Lemaître-Tolman-Bondi Cosmological Model with Cosmological Constant. Int J Theor Phys 53, 181–187 (2014). https://doi.org/10.1007/s10773-013-1795-9
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DOI: https://doi.org/10.1007/s10773-013-1795-9