  Motivated by the relative lack of neutral hydrogen around Lyman Break
Galaxies deduced from recent observations, we investigate the properties of the
Lyalpha forest around high redshift galaxies. The study is based on improved
numerical SPH simulations implementing, in addition to standard processes, a
new scheme for multiphase and outflow physics description. Although on large
scales our simulations reproduce a number of statistical properties of the IGM
(because of the small filling factor of shock-heated gas), they underpredict
the Lyalpha optical depth decrease inside 1 Mpc/h of the galaxies by a factor
of ~2. We interpret this result as due to the combined effect of infall
occurring along the filaments, which prevents efficient halo gas clearing by
the outflow, and the insufficient increase of (collisional) hydrogen ionization
produced by the temperature increase inside the hot, outflow-carved bubble.
Unless an observational selection bias is present, we speculate that local
photoionization could be the only viable explanation to solve the puzzle.
