MASS VARIATION FORMULAS FOR EINSTEIN-YANG-MILLS-HIGGS AND EINSTEIN-DILATON BLACK-HOLES

We consider the ''first law'' of black hole physics for stationary Ein stein-Yang-Mills-Higgs and Einstein-dilaton theories. It is shown that the mass variation formula involves only global quantities and surfac e terms. Our results hold for arbitrary gauge groups and any structure of the Higgs field multiplets. For purely magnetic field configuratio ns, the extra horizon integrals vanish and the variation of the mass c an be expressed in terms of the usual vacuum contributions and additio nal surface integrals at spacelike infinity.