  We propose the modified version of the canonical energy which was introduced
originally by Hollands and Wald. Our construction depends only on the
Euler-Lagrange expression of the system and thus is independent of the
ambiguity in the Lagrangian. After some comments on our construction, we
briefly mention on the relevance of our construction to the boundary
information metric in the context of the AdS/CFT correspondence. We also study
the stability of three-dimensional hairy extremal black holes by using our
construction.
