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 As 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.
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