Frame dragging (Lense-Thirring effect) is generally associated with rotating astrophysical objects. However, it can also be generated by electromagnetic fields if electric and magnetic fields are simultaneously present. In most models of astrophysical objects, macroscopic charge neutrality is assumed and the entire electromagnetic field is characterized in terms of a magnetic dipole component. Hence, the purely electromagnetic contribution to the frame dragging vanishes. However, strange stars may possess independent electric dipole and neutron stars independent electric quadrupole moments that may lead to the presence of purely electromagnetic contributions to the frame dragging. Moreover, recent observations have shown that in stars with strong electromagnetic fields, the magnetic quadrupole may have a significant contribution to the dynamics of stellar processes. As an attempt to characterize and quantify the effect of electromagnetic frame-dragging in these kind of astrophysical objects, an analytic solution to the Einstein-Maxwell equations is constructed here on the basis that the electromagnetic field is generated by the combination of arbitrary magnetic and electric dipoles plus arbitrary magnetic and electric quadrupole moments. The effect of each multipole contribution on the vorticity scalar and the Poynting vector is described in detail. Corrections on important quantities such the innermost stable circular orbit (ISCO) and the epicyclic frequencies are also considered.

A full-relativistic approach is used to compute the radius of the innermost stable circular orbit (ISCO), the Keplerian, frame-dragging, precession and oscillation frequencies of the radial and vertical motions of neutral test particles orbiting the equatorial plane of a magnetized neutron star. The space-time around the star is modelled by the six parametric solution derived by Pachón et al. (2012) It is shown that the inclusion of an intense magnetic field, such as the one of a neutron star, have non-negligible effects on the above physical quantities, and therefore, its inclusion is necessary in order to obtain a more accurate and realistic description of physical processes, such as the dynamics of accretion disks, occurring in the neighbourhood of this kind of objects. The results discussed here also suggest that the consideration of strong magnetic fields may introduce non-negligible corrections in, e.g., the relativistic precession model and therefore on the predictions made on the mass of neutron stars.