  We derive general formulae for the first order variation of the ADM mass,
angular momentum for linear perturbations of a stationary background in
Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the
heterotic string theory. All these variations were expressed in terms of the
perturbed matter energy momentum tensor and the perturbed charge current
density. Combining these expressions we reached to the form of the {\it
physical version} of the first law of black hole dynamics for the stationary
black holes in the considered theory being the strong support for the cosmic
censorship.
