  Current models of gamma-ray lightcurves in pulsars suffer from large
uncertainties on the precise location of particle acceleration and radiation.
Here, we present an attempt to alleviate these difficulties by solving for the
electromagnetic structure of the oblique magnetosphere, particle acceleration,
and the emission of radiation self-consistently, using 3D spherical
particle-in-cell simulations. We find that the low-energy radiation is
synchro-curvature radiation from the polar-cap regions within the light
cylinder. In contrast, the high-energy emission is synchrotron radiation that
originates exclusively from the Y-point and the equatorial current sheet where
relativistic magnetic reconnection accelerates particles. In most cases,
synthetic high-energy lightcurves contain two peaks that form when the current
sheet sweeps across the observer's line of sight. We find clear evidence of
caustics in the emission pattern from the current sheet. High-obliquity
solutions can present up to two additional secondary peaks from energetic
particles in the wind region accelerated by the reconnection-induced flow near
the current sheet. The high-energy radiative efficiency depends sensitively on
the viewing angle, and decreases with increasing pulsar inclination. The
high-energy emission is concentrated in the equatorial regions where most of
the pulsar spindown is released and dissipated. These results have important
implications for the interpretation of gamma-ray pulsar data.
