  We have numerically investigated whether or not a mean-field theory of spin
textures generate fictitious flux in the doped two dimensional $t-J$-model.
First we consider the properties of uniform systems and then we extend the
investigation to include models of striped phases where a fictitious flux is
generated in the domain wall providing a possible source for lowering the
kinetic energy of the holes. We have compared the energetics of uniform systems
with stripes directed along the (10)- and (11)-directions of the lattice,
finding that phase-separation generically turns out to be energetically
favorable. In addition to the numerical calculations, we present topological
arguments relating flux and staggered flux to geometric properties of the spin
texture. The calculation is based on a projection of the electron operators of
the $t-J$ model into a spin texture with spinless fermions.
