2021/08/25 by F. Gholami, Fateme Gholami, Gholami, F. +10
Mathematics · Physics and Astronomy · #Bar (unit) #Combinatorics #Cosmological constant #Cosmology and Gravitation Theories #Dimension (graph theory) #Einstein #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Physics #Product (mathematics) #Relativity and Gravitational Theory #Space (punctuation) #advanced mathematical theories #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2108.11437
14 pages
arxiv created 2021/08/25 · openalex publication_date 2021/08/25 · arxiv updated 2021/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new kind of super warped product spaces M_(I)=I1|0×f Mm|n, M_(II)=I0|1×f Mm|n, and M_(III)=I1|1×f Mm|n, where Mm|n is a supermanifold of dimension m|n, Iδ|δ' is standard superdomain with I=(0,1) and δ,δ' ∈ \0,1\, subject to the warp functions f(t), f( t), and f(t, t), respectively. In each super warped product space, M_(I), M_(II), and M_(III), it is shown that Einstein equations GAB=-ΛgAB, with cosmological term Λ are reducible to the Einstein equations Gαβ = -Λgαβ on the super space Mm|n with cosmological term Λ, where Λ and Λ are functions of f(t), f( t), and f(t, t), as well as (m, n). This dependence points to the origin of cosmological terms which turn out to be within the warped structure of the super space-time. By using the Generalized Robertson-Walker space-time, as a super space-time, and demanding for constancy of Λ we can determine the warp functions and Λ which result in finding the solutions for Einstein equations GAB=-ΛgAB and Gαβ = -Λgαβ. We have discussed the cosmological solutions, for each kind of super warped product space, in the special case of M3|0.