  We show that in a Randall-Sundrum II type braneworld, the vacuum exterior of
a spherical star is not in general a Schwarzschild spacetime, but has
radiative-type stresses induced by 5-dimensional graviton effects. Standard
matching conditions do not lead to a unique exterior on the brane because of
these 5-dimensional graviton effects. We find an exact uniform-density stellar
solution on the brane, and show that the general relativity upper bound
$GM/R<{4\over9}$ is reduced by 5-dimensional high-energy effects. The existence
of neutron stars leads to a constraint on the brane tension that is stronger
than the big bang nucleosynthesis constraint, but weaker than the Newton-law
experimental constraint. We present two different non-Schwarzschild exteriors
that match the uniform-density star on the brane, and we give a uniqueness
conjecture for the full 5-dimensional problem.
