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The formula existing in the literature for the ADM mass of 2D dilaton gravityis incomplete. For example, in the case of an infalling matter shockwave thisformula fails to give a time-independent mass, unless a very special coordinatesystem is chosen. We carefully carry out the canonical formulation of 2Ddilaton gravity theories (classical, CGHS and RST). As in 4D general relativityone must add a boundary term to the bulk Hamiltonian to obtain a well-definedvariational problem. This boundary term coincides with the numerical value ofthe Hamiltonian and gives the correct mass which obviously is time-independent.Comment: revised, 12 pages, PUPT-1379; we added a reference and corrected some  minor typo

Hamiltonian approach to two-dimensional dilaton gravities and invariant ADM mass