  Guillemot et al. recently reported the discovery of $\gamma$-ray pulsations
from the 22.7ms pulsar (pulsar A) in the famous double pulsar system
J0737-3039A/B. The $\gamma$-ray light curve (LC) of pulsar A has two peaks
separated by approximately half a rotation, and these are non-coincident with
the observed radio and X-ray peaks. This suggests that the $\gamma$-ray
emission originates in a part of the magnetosphere distinct from where the
radio and X-ray radiation is generated. Thus far, three different methods have
been applied to constrain the viewing geometry of pulsar A (its inclination and
observer angles $\alpha$ and $\zeta$): geometric modelling of the radio and
$\gamma$-ray light curves, modelling of the position angle sweep in phase seen
in the radio polarisation data, and independent studies of the time evolution
of the radio pulse profile of pulsar A. These three independent, complementary
methods have yielded consistent results: pulsar A's rotation axis is likely
perpendicular to the orbital plane of the binary system, and its magnetic axis
close to lying in the orbital plane (making this pulsar an orthogonal rotator).
The observer is furthermore observing emission close to the magnetic axis. Thus
far, however, current models could not reproduce all the characteristics of the
radio and $\gamma$-ray light curves, specifically the large radio-to-$\gamma$
phase lag. In this paper we discuss some preliminary modelling attempts to
address this problem, and offer ideas on how the LC fits may be improved by
adapting the standard geometric models in order to reproduce the profile
positions more accurately.
