# Covariant and contravariant

## Main Question or Discussion Point

If the notions of covariant and contravariant tensors were not introduced,what would happen?E.g. what form will the Einstein E.q. Guv=8πTuv be changed into ?

Related Special and General Relativity News on Phys.org
PeterDonis
Mentor
2019 Award
If the notions of covariant and contravariant tensors were not introduced,what would happen?
I'm not sure what you mean by this. Covariant and contravariant tensors represent distinct kinds of physical things; if you know the metric, you can compute correspondences between them, but they are still distinct concepts. So if you're going to use tensors at all, you need both kinds.

If the OP is asking whether we could express Guv=8πTuv without tensors, I would have to say that it can be done, but the central property of coordinate independence would still be there ( ie 'tensoriality').

WannabeNewton
The notion of contravariant and covariant is always there. It is made explicit in index notation but you can just as well write it in index-free notation as $G = 8\pi T$ but you cannot get rid of the tensorial nature of the classical EFEs. The extension of the concept of a tensor is a spinor: http://en.wikipedia.org/wiki/Spinor