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\noindent Let $M\to N$ (resp.\ $C\to N$) be the fibre bundle ofpseudo-Riemannian metrics of a given signature (resp.\ the bundle of linearconnections) on an orientable connected manifold $N$. A geometrically definedclass of first-order Ehresmann connections on the product fibre bundle$M\times_NC$ is determined such that, for every connection $\gamma $ belongingto this class and every $\mathrm{Diff}N$-invariant Lagrangian density $\Lambda$ on $J^1(M\times_NC)$, the corresponding covariant Hamiltonian $\Lambda^\gamma $ is also $\mathrm{Diff}N$-invariant. The case of$\mathrm{Diff}N$-invariant second-order Lagrangian densities on $J^2M$ is alsostudied and the results obtained are then applied to Palatini andEinstein-Hilbert Lagrangians.

Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection