  We consider static, spherically symmetric solutions of general relativity
with a nonlinear sigma model (NSM) as a source, i.e., a set of scalar fields
$\Phi = (\Phi^1,...,\Phi^n)$ (so-called chiral fields) parametrizing a target
space with a metric $h_{ab}(\Phi)$. For NSM with zero potential $V(\Phi)$, it
is shown that the space-time geometry is the same as with a single scalar field
but depends on $h_{ab}$. If the matrix $h_{ab}$ is positive-definite, we obtain
the Fisher metric, originally found for a canonical scalar field with positive
kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar
field, including singular and nonsingular horizons (of infinite area) and
wormholes. In particular, the Schwarzschild metric can correspond to a
nontrivial chiral field configuration, which in this case has zero
stress-energy. Some explicit examples of chiral field configurations are
considered. Some qualitative properties of NSM configurations with nonzero
potentials are pointed out.
