Global properties of static spherically symmetric charged dilaton spacetimes with a Liouville potential

We derive the global properties of static spherically symmetric solutions to the Einstein-Maxwell-dilaton system in the presence of an arbitrary exponential dilaton potential. We show that – with the exception of a pure cosmological constant `potential’ – no asymptotically flat, asymptotically de Sitter or asymptotically anti-de Sitter solutions exist in these models.