Cosmological and static spherically symmetric solutions to Einstein equations with an exponential scalar potential

Exponential potentials can be associated both with expanding and collapsing cos- mologies: whereas power-law inflation can be obtained for a nearly flat exponential potential, a stable contracting cosmology (which, by the way, can solve the hori- zon problem) can be obtained for a negative sufficiently steep exponential potential. Motivated by these results, we study the Einstein equation for a scalar field with an exponential potential in a static and spherically symmetric spacetime. For the same parameters which describe a stable contracting cosmology, we find a non- asymptotically flat black hole and we study its properties.