  We use the Klein-Gordon equation in a curved spacetime to construct the
relativistic analog of the Schr\"odinger-Newton problem, where a scalar
particle lives in a gravitational potential well generated by its own
probability distribution. A static, spherically symmetric metric is computed
from the field equations of general relativity, both directly and as modeled by
a perfect-fluid assumption that uses the Tolman-Oppenheimer-Volkov equation for
hydrostatic equilibrium of the mass density. The latter is appropriate for a
Hartree approximation to the many-body problem of a bosonic star. Simultaneous
self-consistent solution of the Klein--Gordon equation in this curved spacetime
then yields solitons with a range of radial excitations. We compare results
with the nonrelativistic case.
