  In Horava-Lifshitz gravity, regularity of a solution requires smoothness of
not only the spacetime geometry but also the foliation. As a result, the
regularity condition at the center of a star is more restrictive than in
general relativity. Assuming that the energy density is a piecewise-continuous,
non-negative function of the pressure and that the pressure at the center is
positive, we prove that the momentum conservation law is incompatible with the
regularity at the center for any spherically-symmetric, static configurations.
The proof is totally insensitive to the structure of higher spatial curvature
terms and, thus, holds for any values of the dynamical critical exponent $z$.
Therefore, we conclude that a spherically-symmetric star should include a
time-dependent region near the center. We also comment on the condition under
which linear instability of the scalar graviton does not show up.
