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Timelike Killing vectors are associated with conservation of energy, and space-like Killing vectors with the conservation of momentum quantities.

But the energy-momentum tensor is always 'conserved' - well in GR, this goes to it's divergence being zero.

And , the FRW metric does not possess a time-like Killing vector - so energy is not conserved.

It possess space-like ones, and momentum is thus conserved.

But, how then, is the energy-momentum tensor conserved?

Depending on the geometry of the space, are there cases when momentum and energy are conserved seperately, and so energy-momentum is conserved, but also cases where the energy-momentum is only conserved as a single quantity. So a Killing vector could not suffice to give this conserved quantity. Instead would it be described by a Killing tensor?

Thanks in advance.

But the energy-momentum tensor is always 'conserved' - well in GR, this goes to it's divergence being zero.

And , the FRW metric does not possess a time-like Killing vector - so energy is not conserved.

It possess space-like ones, and momentum is thus conserved.

But, how then, is the energy-momentum tensor conserved?

Depending on the geometry of the space, are there cases when momentum and energy are conserved seperately, and so energy-momentum is conserved, but also cases where the energy-momentum is only conserved as a single quantity. So a Killing vector could not suffice to give this conserved quantity. Instead would it be described by a Killing tensor?

Thanks in advance.

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