| This thesis addresses some classical and semi-classical aspects of black holes, using an effective membrane representation of the event horizon. This “membrane paradigm” is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here, however, the equations are derived from an underlying action formulation which has the advantage of clarifying the paradigm and simplifying the derivations, in addition to providing a bridge to thermodynamics and quantum mechanics. Within this framework, previous membrane results are derived and extended to dyonic black hole solutions. It is explained how an action can produce dissipative equations. The classical portion of the study ends with a demonstration of the validity of a minimum entropy production principle for black holes.; Turning next to semi-classical theory, it is shown that familiar thermodynamic properties of black holes also emerge from the membrane action, via a Euclidean path integral. In particular, the membrane action can account for the hole's Bekenstein-Hawking entropy, including the numerical factor. Two short and direct derivations of Hawking radiation as an instanton process are then presented. The first is a tunneling calculation based on particles in a dynamical geometry, closely analogous to Schwinger pair production in an electric field. The second derivation makes use of the membrane representation of the horizon. In either approach, the imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. But because these derivations respect conservation laws, the exact result contains a qualitatively significant correction to Hawking's thermal spectrum.; Finally, by extending the charged Vaidya metric to cover all of spacetime, a Penrose diagram for the formation and evaporation of a charged black hole is obtained. It is found that the spacetime following the evaporation of a black hole is predictable from initial conditions, provided that the dynamics of the time-like singularity can be calculated. |
