This dissertation contains two works; one of the behavior of dynamical electromagnetic fields in the stationary spacetime generated by a black hole, and the other on the structure of a general stationary vacuum spacetime itself.
The study of electromagnetic field is carried out in terms of the "membrane formalism" for black holes; and it is part of a series of papers with the aim of developing that formalism into a complete, self-consistent description of electromagnetic and gravitational fields in a black hole background. Various model problems are presented as aids in understanding the interactions of electromagnetic fields with a black hole, and special attention is paid to the concept of the "stretched horizon" which is vital for the membrane formalism.
The second work develops a multipole moment formalism for a general stationary system in general relativity. The multipole moments are defined in terms of a general formal series solution of the stationary Einstein equation, in analogy to multipole moments in the Newtonian theory of gravity. These relativistic moments exhibit many desirable properties and are shown to be useful in studying the interactions between a gravitating body and an external gravitational field. A model calculation applying the formalism to a black hole interacting with an external multipole field shows that the interaction can be understood in terms of "elastic moduli" of the black-hole horizon.
