I have seen a few posts here on stack exchange that suggest that energy is not conserved in general relativity on a large scale.

I am a pretty confused with this. I don’t understand how such a conclusion is reached.

$\nabla_\mu T^{\mu\nu}$ $=0$

Doesn’t the above equation signify that energy momentum is conserved in GR.

Please note there are other questions already on such issues. But they seem to suggest that energy is not conserved in GR.

See for eg: If the energy of the photon is conserved along a geodesic why is it redshifted

But I am asking that when we have $\nabla_\mu T^{\mu\nu}$ $=0$ why will energy not be conserved in the first place itself

Edit after the comment:

I am asking why $\nabla_\mu T^{\mu\nu}$ $=0$ does not imply energy conservation

  • $\begingroup$ I am not familiar with the mathematics of GR, but is the above equation true between reference frames or only in one reference frame? $\endgroup$
    – Jonas
    Feb 8 at 12:59
  • $\begingroup$ @Jonas It is an equation so it’s valid in an reference frame. If I had a partial derivative instead of a covariant derivative then it would have been valid in just an inertial frame. $\endgroup$
    – Shashaank
    Feb 8 at 13:02
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    $\begingroup$ @Oбжорoв Read the question again. I know that a conserved quantity can be constructed from a killing vector. I am asking why the vanishing of covariant derivative of energy momentum tensor not imply energy conservation. $\endgroup$
    – Shashaank
    Feb 8 at 13:05
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    $\begingroup$ Also possible duplicates: physics.stackexchange.com/q/2597, physics.stackexchange.com/q/109532 $\endgroup$ Feb 8 at 13:08
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    $\begingroup$ @Eletie I vaguely understand what you are saying in your comment. I guess things would be clearer if the explanation is expanded a bit. If you would like to put and answer, I will be glad to accept it. $\endgroup$
    – Shashaank
    Feb 8 at 13:50