On Gravity, Torsion and the Spectral Action Principle
  We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points. 
Frank Pfaeffle and Christoph A. Stephan
math-ph math.MP