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

TL;DR

This paper provides a detailed canonical analysis of n-dimensional f(Riemann) gravity, correcting previous results, and reformulates the field equations to identify non-stationary energy, with examples including R^2 and Ricci tensor squared theories.

Contribution

It offers a corrected and detailed canonical framework for f(Riemann) gravity and reformulates the field equations for energy analysis, advancing theoretical understanding.

Findings

Corrected earlier canonical analyses of f(Riemann) gravity.

Reformulated field equations in Fischer-Marsden form for energy identification.

Applied methods to R^2 and Ricci tensor squared theories.

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.