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- W1620834443 abstract "It is well known [] that the three-dimensional space $$ {d^{(3)}}{8^2} = {{d{r^2}} over {1 - {{{r^2}} over {{R^2}}}}} + {r^2}(d{vartheta ^2} + {sin ^2}vartheta d{varphi ^2}) $$ (1) of some models of closed homogeneous and isotropic universes has an especially simple geometry which can be seen best introducing a angular coordinate 0 ≤ ϰ ≤ π via r = R sin ϰ and transforming the line element (1) into the form $$ {d^{(3)}}{8^2} = {R^2}(d{chi ^2} + {sin ^2}chi d{Omega ^2}) $$ (2) where $$ d{Omega ^2} = d{vartheta ^2} + {sin ^2}vartheta d{varphi ^2} $$ (3) The metric (2) is that of a three-dimensional hypersurface of radius R which can be represented in a flat, four-dimensional Euclidean embedding space." @default.
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- W1620834443 date "2001-01-01" @default.
- W1620834443 modified "2023-09-27" @default.
- W1620834443 title "Schwarzschild Metrics, Quasi-Universes and Wormholes" @default.
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