General relativity is strongly based on the concept of diffeomorphism.
However diffeomorphisms are not linear.
I wish to recover as much of general relativity as possible, but while remain linear.
I understand that there are generalizations of gravity (metric-affine for instance), but here I am interested in a reduction to the general linear group.
Can I formulate a theory (hopefully as close to the original as possible) of gravity based on the general linear group, instead of diffeomorphism.