Elements of the Metric–Affine gravity I: Aspects of F(R) theories reductions and the topologically massive gravity

Some classical aspects of Metric–Affine Gravity are reviewed in the context [Formula: see text] type models (polynomials degree Riemann tensor) and topologically massive gravity. At nonperturbative level, we explore consistency field equations when reduced to a Riemann–Christoffel (RCh) space–time, either via Riemann–Cartan (RC) space or an Einstein–Weyl (EW) space. It is well known for case that any path reduction “classes” RC EW leads same with exception theories text]. We verify this discrepancy can be solved by imposing nonmetricity torsion constraints. In particular, interest expected physical solutions as those conformally flat class. On other hand, symmetries gravity reviewed, content scenarios. The appearance nonlinearly modified selfdual model existence many nonunitary degrees freedom suggestion which cure unphysical propagations shall discussed.