By requiring the inner product in two points ##x## and ##x'## having metrics ##g## and ##g'## to be invariant, i.e. ##g'(x') = g(x)##, one is lead to the Killing equation. Does general relativity forbiddes spaces where the Killing equation cannot be satisfied?(adsbygoogle = window.adsbygoogle || []).push({});

It seems obvious that we want conserved quantities in our theories. But, is there a way around in which we can consider a space-time having no Killing Vectors at all?

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# I Existence of Killing vectors

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