  We introduce a set of constraint preserving boundary conditions for the
Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution
equations in spherical symmetry, based on its hyperbolic structure. While the
outgoing eigenfields are left to propagate freely off the numerical grid,
boundary conditions are set to enforce that the incoming eigenfields don't
introduce spurious reflections and, more importantly, that there are no fields
introduced at the boundary that violate the constraint equations. In order to
do this we adopt two different approaches to set boundary conditions for the
extrinsic curvature, by expressing either the radial or the time derivative of
its associated outgoing eigenfield in terms of the constraints. We find that
these boundary conditions are very robust in practice, allowing us to perform
long lasting evolutions that remain accurate and stable, and that converge to a
solution that satisfies the constraints all the way to the boundary.
