Supersymmetric black holes are extremal and bald in 2D dilaton supergravity

We prove that solutions of 2D dilaton supergravity respecting both supersymmetries have to belong to the rather trivial class of constant dilaton vacua. Then it is shown that solutions which retain at least half of the supersymmetries are ground states with respect to the bosonic Casimir function – in physical terms, the ADM mass has to vanish, whenever this notion is meaningful. Nevertheless, by tuning the prepotential appropriately, black hole solutions may emerge in such ground states with an arbitrary number of (Killing) horizons. Exploiting supersymmetric obstructions for bosonic quantities it is proven that all horizons have to be extremal. In these derivations the knowledge of the general analytic solution of 2D dilaton supergravity plays an important rôle. Finally it is demonstrated that the inclusion of non-minimally coupled matter, a step which is already nontrivial by itself, does not change these features in an essential way. As byproducts we notice the impossibility of a supersymmetric dS ground state even in the presence of a dilaton, and the absence of dilatino and gravitino hair for all supersymmetric black holes. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]