>You can have a tensor R(x,y) that tells you the curvature of the rubber sheet as a function of position (x,y). And a scalar T(x,y) that tells you the temperatu

>You can have a tensor R(x,y) that tells you the curvature of the rubber sheet as a function of position (x,y). And a scalar T(x,y) that tells you the temperature of the rubber sheet at (x,y). These are completely independent quantities. Different fields. I get that it's an analogy, but I don't think they would be completely independent quantities here. There is likely going to be some correlation with temperature and curvature of the rubber sheet. It would likely pale in comparison to almost everything else though, but on the topic of discussion that might be a large enough correlation. Also, don't high energy photons curve spacetime?