Constraints and Time Evolution in Generic $f$(Riemann) Gravity

Abstract

We give a detailed canonical analysis of the $n$-dimensional $f$(Riemann) gravity, correcting the earlier results in the literature. We also write the field equations in the Fischer-Marsden form which is amenable to identifying the non-stationary energy on a spacelike hypersurface. We give pure $R^{2}$ and $R_{\mu\nu}R^{\mu\nu}$ theories as examples.