Finally! I have changed from a consumer of scientific progress to a producer thereof: my first respectable paper has been posted to arXiv. It is on "A space-time characterization of the Kerr-Newman metric".

Following a result of Marc Mars, I examined the question of "what makes a pseudo-stationary Einstein-Maxwell space-time a member of the Kerr-Newman family?" I found that I can devise two tensorial quantities (one a space-time two-form that measures the alignment of the electro-magnetic field with the pseudo-electro-magnetic field generated by the stationarity condition; the other a four-tensor that measures the alignment of the electro-magnetic field with the gravitational radiation field) whose simultaneous vanishing (meaning that the relevant quantities are completely aligned) implies that the space-time is Kerr-Newman.

The principal tool in the analysis is direct calculation using a tetrad formalism that is similar to the Newman-Penrose one, but has the advantage of notational symmetries that compactifies the equations. To be more precise, I only need to calculate half as many quantities in this formalism due to some natural symmetries of the space-time (especially in the Einstein-Maxwell case) as I would need were I to use the Newman-Penrose formalism.