Could anyone give me some references for mathematicians (coordinates free notation, formalism of fiber bundles etc.) about tetrads, Palatini-Cartan theory, stuff about formulation of GR with tetrads?
Thanks.
2026-02-22 21:21:23.1771795283
Book on tetrads formalism and tetradic formulation of General Relativity
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Personally I do know only two references:
1) "Natural and gauge natural formalism for classical field theories" by L.Fatibene, M. Francaviglia.
2) "Gravity, a geometrical course volume I" by P.G. Frè
The first is the better one to me (even though it heavily uses coordinates) tetrads are studied in 8.7 and Palatini is in 7.8, but the book is a very good introduction to classical field theory with jet formalism. The second is written in a more intrinsic fashion, however it is for physicists, and is not very consistent (e.g. it goes on confusing spin connections with $SO(1,n-1)$-connections).
If however you are more interested in the geometry behind tetrad like structures, you maybe would like to study $G$-structures for manifolds.
Hope this is somewhat of help.