Kartik Prabhu
replied to a post on Twitter with
The canonical energy as given in Hollands-Wald is gauge-invariant up to “boundary terms”. To avoid this awkwardness, Hollands-Wald partially fix the gauge at the horizon (and infinity appropriately) by requiring vanishing perturbed area and perturbed expansion. One can choose to not gauge-fix but instead modify the canonical energy definition itself by adding certain boundary terms so that the modified one is completely gauge-invariant.
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