BOGOMOLNYI-TYPE MASS FORMULAS FOR A CLASS OF NONROTATING BLACK-HOLES

In the presence of a Killing symmetry, various self-gravitating field theories with massless scalars (moduli) and vector fields reduce to si gma models, effectively coupled to three-dimensional gravity. We argue that this particular structure of the Einstein-matter equations gives rise to quadratic relations between the asymptotic flux integrals and the area and surface gravity (Hawking temperature) of the horizon. Th e method is first illustrated for the Einstein-Maxwell system. A deriv ation of the mass formula is then also presented for the Einstein-Maxw ell-dilaton-axion model, which is relevant to the bosonic sector of he terotic string theory.