Experimental Tests of GR for Non-Vanishing Tensor

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SUMMARY

Experimental tests of the Einstein field equations for non-vanishing energy-momentum tensors have been limited, with significant references found in cosmology and neutron star studies. The discussion highlights the importance of metrics such as the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and the Reissner-Nordström/Kerr-Newman metrics in understanding these tests. The inquiry raises the question of whether Einstein-Maxwell theory should be classified as a theory rather than a hypothesis, indicating a need for further exploration in this area.

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Geometry_dude
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My question is the following: Have there ever been any experimental tests of the Einstein equation (a.k.a. Einstein field equations) for the case of non-vanishing energy-momentum tensor?
If so, which ones?

I know there's a wikipedia article about tests of general relativity and I have already employed the search function here and of course google, but couldn't find anything specific.
 
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Cosmology. Neutron stars.
 
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Thank you for your answer. I suppose you mean the following corresponding metrics
  • FLRW metric
  • Reissner-Nordström/Kerr-Newman metric
Does the latter imply that Einstein-Maxwell theory should be considered a theory as opposed to an hypothesis?
 

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