An exact correspondence between a black hole and an accelerating mirror is demonstrated.It is shown that for a massless minimally coupled scalar field the same Bogolubov coefficients connecting the in and out states occur for a (1+1)D flat spacetime with a particular perfectly reflecting accelerating boundary trajectory and a (1+1)D curved spacetime in which a null shell collapses to form a black hole. Generalization of the latter to the (3+1)D case is discussed. The spectral dynamics is computed in both (1+1)-dimensional spacetimes along with the energy flux in the spacetime with a mirror. It is shown that the approach to equilibrium is monotonic, asymmetric in terms of the rate, and there is a specific time which characterizes the system when it is the most out-of-equilibrium.

Particle production due to a quantized, massless, minimally coupled scalar field in two-dimensional flat spacetime with an accelerating mirror is investigated, with a focus on the time dependence of the process. We analyze first the classes of trajectories previously investigated by Carlitz and Willey and by Walker and Davies. We then analyze four new classes of trajectories, all of which can be expressed analytically and for which several ancillary properties can be derived analytically. The time dependence is investigated through the use of wave packets for the modes of the quantized field that are in the out vacuum state. It is shown for most of the trajectories studied that good time resolution of the particle production process can be obtained.

A new solution of a unitary moving mirror is found to produce finite energy and emit thermal radiation despite the absence of an acceleration horizon. In the limit that the mirror approaches the speed of light, the model corresponds to a black hole formed from the collapse of a null shell. For speeds less than light, the black hole correspondence, if it exists, is that of a remnant. 4 Note that there are two types of black hole remnant in the literature: the "long-lived" or "metastable" remnant, and the "eternal" remnant [31] . The former has lifetime much longer than that of a black hole, that is, proportional to M n where n > 3. An eternal remnant, on the other hand, lives forever. Our model corresponds to an eternal red-shifted scenario.5 Einstein's gravity is topological in (1+1)-dimensions, but with a suitable coupling to matter fields, gravity need not be trivial in (1+1)-dimensions. This allows one to study black hole evaporation. In our moving mirror model, of course, there is no gravity, only an accelerating mirror, so there is no complication either.

We investigate superfluidity, and the mechanism for creation of quantized vortices, in the relativistic regime. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics gives rise to superfluidity. The mechanisms discussed are local inertial forces (Coriolis and centrifugal), and current-current interaction with an external source. The primary application is to cosmology, but we also discuss the reduction to the nonrelativistic nonlinear Schrödinger equation, which is widely used in describing superfluidity and vorticity in liquid helium and cold-trapped atomic gases.