EXTREMAL BLACK-HOLES AS BOUND-STATES

We consider a simple static extremal multi-black hole solution with co nstituents charged under different U(1) fields, Each of the constituen ts by itself is an extremal dilatonic black hole of coupling a = root 3. For a special case with two electrically and two magnetically charg ed black holes the multi-black hole solution interpolates between the familiar a = root 3, 1, 1/root 3 and 0 solutions, depending on how man y black holes are placed at infinity. This proves the hypothesis that black holes with the above dilaton couplings arise in string theory as bound states of fundamental a = root 3 states with zero binding energ y. We also generalize the result to states where the action does not a dmit a single scalar truncation and show that a wide class of dyonic b lack holes in toroidally compactified string theory can be viewed as b ound states of fundamental a = root 3 black holes.