Relativistic electrodynamics of spinning compact objects

A theoretical study of some electrodynamic features of a region close to a slowly-rotating magnetized relativistic star is performed. To be a little more specific, based on the solution-generating method given by Wald, the magnetic fields around both uncharged and (slightly) charged relativistic stars have been obtained. Particularly for a charged relativistic star, again following the argument by Wald, the star was shown to gradually accrete charge until it reached an equilibrium value (Q) over tilde = 2B(0)J. This value of the equilibrium charge seems to be generic as a rotating black hole is known to accrete exactly the same amount. Although these results are equally relevant to all species of slowly-rotating relativistic Stars, we particularly have the rotating neutron star in mind. As such, it would be of some interest to attempt to make contact with a real pulsar case. Thus, we discuss how many of the theoretical results obtained in the present work can be carried over to a realistic, general relativistic description of a pulsar's magnetosphere.