Friedmann-Lemaître-Robertson-Walker spaces as submanifolds of $\mathbb{R}^6$: Restriction to the Klein-Gordon operator

Abstract : The Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes can be realized as submanifolds of R6. In this paper, we relate the Laplace-Beltrami operator for a homogeneous scalar field ϕ of R6 to its explicit restriction on FLRW spacetimes. We then make the link between the homogeneous solutions of the equation □6ϕ=0 in R6 and those of the Klein-Gordon equation (□f−ξRf+m2)ϕf=0 for the free field ϕf in the FLRW spacetime. We obtain as a byproduct a formula for the Ricci scalar of the FLRW spacetime in terms of the function f defining this spacetime in R6.
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https://hal.archives-ouvertes.fr/hal-01669643
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Soumis le : mercredi 20 décembre 2017 - 23:50:04
Dernière modification le : lundi 23 juillet 2018 - 02:27:47

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J.P. Zapata, A. Belokogne, E. Huguet, J. Queva, J. Renaud. Friedmann-Lemaître-Robertson-Walker spaces as submanifolds of $\mathbb{R}^6$: Restriction to the Klein-Gordon operator. J.Math.Phys., 2017, 58 (11), pp.113503. 〈10.1063/1.4998179〉. 〈hal-01669643〉

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