Near-thermal radiation in detectors, mirrors, and black holes: A stochastic approach

In analyzing the nature of thermal radiance experienced by an accelerated observer (Unruh effect), an eternal black hole (Hawking effect), and in certain types of cosmological expansion, one of us proposed a unifying viewpoint that these can be understood as arising from the vacuum fluctuations of the quantum field being subjected to an exponential scale transformation in these systems. This viewpoint, together with our recently developed stochastic theory of particle-field interaction understood as quantum open systems described by the influence functional formalism, can be used effectively to address situations where the spacetime possesses an event horizon only asymptotically, or none at all. Examples studied here include detectors moving at uniform acceleration only asymptotically or for a finite time, a moving mirror, and a two-dimensional collapsing mass. We show that in such systems radiance indeed is observed, albeit not in a precise Planckian spectrum. The deviation therefrom is determined by a parameter which measures the departure from uniform acceleration or from exact exponential expansion. The methodology illustrated here is expected to be useful for the investigation of nonequilibrium black hole thermodynamics and the linear response regime of back reaction problems in semiclassical gravity.