Asymptotics in the time-dependent Hawking and Unruh effects - Juárez Aubry, Benito A. (2016)
In this thesis, we study the Hawking and Unruh effects in time-dependent situations, as registered by localised spacetimes observers in several asymptotic situations. In 1+1 dimensions, we develop the Unruh-DeWitt detector model that is coupled to the proper time derivative of a real scalar field. This detector is insensitive to the well-known massless scalar field infrared ambiguity and has the correct massive-to-massless field limit. We then consider three scenarios of interest for the Hawking effect. The first one is an inertial detector in an exponentially receding mirror spacetime, which traces the onset of an energy flux from the mirror, with the expected Planckian late time asymptotics. The second one is the transition rate of a detector that falls in from infinity in Schwarzschild spacetime, gradually losing thermality. We find that the detector's transition rate diverges near the singularity proportionally to r^(-3/2). The third one is the characterisation of the strength of divergence of the transition rate and of the (smeared) renormalised local energy density along a trajectory that approaches the future Cauchy horizon of a (1+1)-dimensional spacetime that generalises the non-extremal Reissner-Nordström spacetime and shares its causal structure. In both cases, the strength of the divergence as a function of the proper time is as on approaching the Schwarzschild singularity. We then comment on the limitations of our (1+1)-dimensional analysis as a model for the full 3+1 treatment. In 3+1 dimensions, we revisit the Unruh effect and study the onset of the Unruh temperature. We treat an Unruh-DeWitt detector coupled to a massless scalar through a smooth switching function of compact support and prove that, while the Kubo-Martin-Schwinger (KMS) condition and the detailed balance of the response are equivalent in the limit of long interaction time, this equivalence is not uniform in the detector's energy gap. That is, we prove that the infinite-time and large-energy limits do not commute. We then ask and answer the question of how long one needs to wait to detect the Unruh temperature up to a prescribed large energy scale. We show that, under technical conditions on the switching function, in this large energy gap regime an adiabatically switched detector following a Rindler orbit will thermalise in a time scale that is polynomially large in the energy. We then consider an interaction between the detector and the field that switches on, interacts constantly for a long time, and then switches off. We show that a polynomially fast thermalisation cannot occur if the constant interaction time is polynomially large in the energy, with the switching tails fixed. Thus, we conclude that the details of the switching are relevant when estimating thermalisation time-scales.