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This note investigates the conditions for twisted space-times in cosmological models, suggesting implications for their classification.
Twisted space-times are logical extensions of Friedmann cosmological models, Lorentz–Minkowski space-times, Einstein-de Sitter space-times, generalized Robertson–Walker (GRW) space-times, and static Einstein space-times. The purpose of this manuscript is to investigate the characteristics of twisted space-times that are almost pseudo-Ricci symmetric (briefly, A(PRS) ₙ ). We establish the sufficient conditions under which A(PRS) ₙ twisted space-times are GRW space-times, and under which A(PRS) ₙ space-times are twisted space-times. The necessary and sufficient condition for A(PRS) ₙ twisted space-times to be perfect fluid space-times is derived. We also prove that the vorticity and shear of A(PRS) ₙ twisted space-times filled with perfect fluid vanish identically. Consequently, we establish the equation of state and energy conditions. The non-existence of Ricci symmetric A(PRS) ₙ twisted space-times is ensured.
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DE et al. (2026) studied this question.
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