  In this paper I examine black hole and cosmological space-times in
Born-Infeld-Einstein theory with electric and magnetic charges. The field
equations are derived and written in the form $G_{\mu\nu}=-\kappa T_{\mu\nu}$
for spherically symmetric space-times. The energy-momentum tensor is not the
Born-Infeld energy-momentum tensor, but can be obtained from Born-Infeld theory
by letting $a\to ia$, where $a$ is the Born-Infeld parameter. It is shown that
there is a curvature singularity in spherically symmetric space-times at a
nonzero radial coordinate and that, as in Reissner-Nordstrom space-times, there
are zero, one or two horizons. Charged black holes have either two horizons and
a timelike singularity or one horizon with a spacelike, timelike, or null
singularity. Anisotropic cosmological solutions with electric and magnetic
fields are obtained from the spherically symmetric solutions.
