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- W3124241417 endingPage "155007" @default.
- W3124241417 startingPage "155007" @default.
- W3124241417 abstract "The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is shown that it is always possible to select a synchronised family of causal geodesics $Gamma$ and an open neighbourhood $mathcal{U}$ of a final segment of $gamma$ in $M$ such that $mathcal{U}$ is comprised by members of $Gamma$, and suitable local coordinates can be defined everywhere on $mathcal{U}$ provided that $gamma$ does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime, $(M,g_{ab})$, is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order $k-1$ are bounded on $mathcal{U}$, and also the line integrals of the components of the $k^{th}$-order covariant derivatives are finite along the members of $Gamma$---where all the components are meant to be registered with respect to a synchronised frame field on $mathcal{U}$---then there exists a $C^{k-}$ extension $Phi: (M,g_{ab}) rightarrow (widehat{M},widehat{g}_{ab})$ so that for each $bargammainGamma$, which is inextendible in $(M,g_{ab})$, the image, $Phicircbargamma$, is extendible in $(widehat{M},widehat{g}_{ab})$. Finally, it is also proved that whenever $gamma$ does terminate on a topological singularity $(M,g_{ab})$ cannot be generic." @default.
- W3124241417 created "2021-02-01" @default.
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- W3124241417 date "2010-06-17" @default.
- W3124241417 modified "2023-09-27" @default.
- W3124241417 title "Spacetime extensions II" @default.
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- W3124241417 doi "https://doi.org/10.1088/0264-9381/27/15/155007" @default.
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