Neutron stars are strongly magnetized rotating compact objects .
Therefore they also produce huge electric fields accelerating particles to ultra-relativistic energies .
The simplest magnetic topology is a dipole traditionally located at the stellar centre .
In this paper , we reinvestigate the consequences of an off-centred rotating magnetic dipole , showing accurate magnetic field line geometries , the associated spin-down luminosity as well as the corresponding electromagnetic kick and torque imprinted to the neutron star .
Results are obtained by time dependent numerical simulations of Maxwell equations in vacuum using pseudo-spectral methods .
We compare our results to known analytical expressions available to lowest order in the parameter \epsilon = d / R , where d is the displacement of the dipole from the stellar centre and R the neutron star radius .
We found good agreement between our numerical computations and our analytical approximations even for well off-centred dipoles having large displacements with a sizeable fraction of the radius , i.e . \epsilon \lesssim 1 .
An explanation for binary neutron star eccentricity distribution functions is given with an emphasize on highly eccentric systems as an alternative scenario to traditional binary formation .