  Axially symmetric stationary metrics governed by the Einstein-Euler equations
for slowly rotating perfect fluids have been constructed in an arbitrarily
large bounded domain containing the support of the mass density. However the
problem of global prolongation of the metric is still open. On the other hand
the so called matter-vacuum matching problem, particularly as the source
problem for the Kerr metric, has been discussed by several authors. This can be
regarded as the approach to the same open problem in the opposite direction. We
give a remark on this open problem.
