Event Horizons, Quantum Mechanics, and the Semiclassical Stability of de Sitter Space.

Quantum effects in the presence of an event horizon are examined in two contexts: first-quantized particle mechanics and quantum field theory in curved space-time. First, the inertial motion of a fermion in Minkowski space is analyzed from the standpoint of a uniformly accelerated observer. The Dirac Hamiltonian of the freely falling particle is derived and used to determine the extent to which classical behavior in the accelerated frame is preserved quantum-mechanically. We find that any wave function with a finite inner product in the accelerated system will necessarily lead to a conserved probability. In addition, the semiclassical limit of the theory is discussed. Spatially homogeneous perturbations of a spatially flat de Sitter metric arising from the fluctuations of a free, massive, scalar quantum field about the Bunch-Davies vacuum state are considered next. The semiclassical Einstein equations are applied to this system and studied to linear order in the perturbations. Solutions consistent with the equation of motion of the scalar field propagating in the perturbed spacetime are obtained. By analyzing the late-time behavior of the metric perturbation, we show that these fluctuations do not render this system unstable. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).