  (Abridged) Gamma-ray emission from pulsars has long been modeled using a
vacuum dipole field. This approximation ignores changes in the field structure
caused by the magnetospheric plasma and strong plasma currents. We present the
first results of gamma-ray pulsar light curve modeling using the more realistic
field taken from 3D force-free magnetospheric simulations. Having the geometry
of the field, we apply several prescriptions for the location of the emission
zone, comparing the light curves to observations. We find that the conventional
two-pole caustic model fails to produce double-peak pulse profiles, mainly
because the size of the polar cap in force-free magnetosphere is larger than
the vacuum field polar cap. The conventional outer-gap model is capable of
producing only one peak under general conditions, because a large fraction of
open field lines does not cross the null charge surface. We propose a novel
"separatrix layer" model, where the high-energy emission originates from a thin
layer on the open field lines just inside of the separatrix that bounds the
open flux tube. The emission from this layer generates two strong caustics on
the sky map due to the effect we term "Sky Map Stagnation" (SMS). It is related
to the fact that force-free field asymptotically approaches the field of a
rotating split monopole, and the photons emitted on such field lines in the
outer magnetosphere arrive to the observer in phase. The double-peak light
curve is a natural consequence of SMS. We show that most features of the
currently available gamma-ray pulsar light curves can be reasonably well
reproduced and explained with the sepatratrix model using the force-free field.
Association of the emission region with the current sheet will guide more
detailed future studies of the magnetospheric acceleration physics.
