  The geometric spin Hall effect of light (GSHEL), similar to the spin Hall
effect of light, is also a spin-dependent shift of the centroid of light beam's
intensity (energy flux), but it is a purely geometric effect that does not
depend on a particular light-matter interaction. In this paper, we discuss the
GSHEL with respect to momentum instead of energy flux, and find out that in the
case of the symmetric energy-momentum tensor, the shift of the centroid of
momentum flux is double that of energy flux. Interestingly, for the canonical
energy-momentum tensor, the centroid shift of momentum flux agrees with that of
energy flux. If we consider the effect of orbital angular momentum, however,
the centroid displacement of momentum flux is twice that of energy flux for
both energy-momentum tensors. To tell which energy-momentum tensor of light
field would be more "correct", we propose a experimental scheme to test the
GSHEL of momentum flux through the mechanical effect of light.
