Most current pulsar emission models assume photon production and emission within the magnetosphere. Low frequency radiation is preferentially produced in the vicinity of the polar caps whereas the high-energy tail is shifted to regions closer but still inside the light-cylinder. We conducted a systematic study of the merit of several popular radiation sites like the polar cap, the outer gap and the slot gap. We computed sky maps emanating from each emission site according to a prescribed distribution function for the emitting particles made of an electron/positron mixture. Calculations are performed using a three dimensional integration of the plasma emissivity in the vacuum electromagnetic field of a rotating centred general-relativistic dipole. We compare Newtonian electromagnetic fields to their general-relativistic counterpart. In the latter case, light bending is also taken into account. As a typical example, light-curves and sky maps are plotted for several power-law indices of the particle distribution function. The detailed pulse profiles strongly depend on the underlying assumption about the fluid motion subject to strong electromagnetic fields. This electromagnetic topology enforces the photon propagation direction directly, or indirectly, from aberration effects. We also discuss the implication of a net stellar electric charge on to the sky maps. Taking into account the electric field strongly affects the light-curves originating close to the light-cylinder where the electric field strength becomes comparable to the magnetic field strength.

Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal. Corrected version