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Time-dependent compactification to de Sitter space: a no-go theorem
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Time-dependent compactification to de Sitter space: a no-go theorem
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It is known that the Einstein gravitational field equations in $D>4$ spacetime dimensions have no time-independent non-singular compactification solutions to de Sitter space if the $D$-dimensional stress tensor satisfies the Strong Energy Condition (SEC). Here we show, by example, that the SEC alone does not exclude time-dependent non-singular compactifications to de Sitter space, in Einstein conformal frame. However, this possibility is excluded by the combined SEC and Null Energy Condition (NEC) because the NEC forces a time-evolution towards a singular $D$-metric.
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Cited by 1 Pith paper
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Holographic timelike complexity for de Sitter
Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.
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