Abstract
In the present paper, we prove a classification (uniqueness) theorem for stationary, asymptotically flat black hole spacetimes with connected and nondegenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling parameter . We show that such black holes are uniquely specified by the length of the horizon interval, angular momentum, electric and magnetic charge, and the value of the dilaton field at infinity when the dilaton coupling parameter satisfies . The proof is based on the nonpositivity of the Riemann curvature operator on the space of the potentials. A generalization of the classification theorem for spacetimes with disconnected horizons is also given.
- Received 27 September 2010
DOI:https://doi.org/10.1103/PhysRevD.82.124050
© 2010 The American Physical Society