  We study possible static non-Schwarzschild exteriors for nonstatic
spherically symmetric stars in a Randall $&$ Sundrum type II braneworld
scenario. Thus, the vacuum region outside the surface of a star is assumed to
be a static solution to the equation $^{(4)}R = 0$, where $^{(4)}R $ is the
scalar curvature of the 4-dimensional Ricci tensor with spherical symmetry.
Firstly, we show that for nonstatic spheres the standard matching conditions
are much more restrictive than for static ones; they lead to a specific
requirement on the vacuum region outside of a nonstatic star, that is absent in
the case of static stars. Secondly, without making any assumption about the
bulk, or the material medium inside the star, we prove the following theorem on
the brane: for {\it any} nonstatic spherical star, without rotation, there are
only two possible static exteriors; these are the Schwarzschild and the
"Reissner-Nordstr{\"o}m-like" exteriors. This is quite distinct from the case
of stars in hydrostatic equilibrium which admit a much larger family of
non-Schwarzschild static exteriors.
