  Using Gutzwiller-projected wave functions, I estimate the ground-state energy
of the t-J model for several variational states relevant for high-temperature
cuprate superconductors. The results indicate antiferromagnetism and phase
separation at low doping both in the superconducting state and in the
staggered-flux normal state proposed for the vortex cores. While phase
separation in the underdoped superconducting state may be relevant for the
stripe formation mechanism, the results for the normal state suggest that
similar charge inhomogeneities may also appear in vortex cores up to relatively
high doping values.
