This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.
