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I am reading through some GR lecture notes and have come across the following:

"A spacetime is static if there exists a coordinate chart where:

∂_{0}g_{μν}= 0

g_{0i}= 0

This spacetime admits a Timelike Killing vector X that satisfies:

X_{[α}∇_{β}X_{γ]}= 0 "

How do I go about proving that this relation is true?

Thanks!

David

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# I Killing Vector Of Static Spacetime

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