We study an Unruh-DeWitt particle detector that is coupled to the proper time derivative of a real scalar field in 1+1 spacetime dimensions. Working within first-order perturbation theory, we cast the transition probability into a regulatorfree form, and we show that the transition rate remains well defined in the limit of sharp switching. The detector is insensitive to the infrared ambiguity when the field becomes massless, and we verify explicitly the regularity of the massless limit for a static detector in Minkowski half-space. We then consider a massless field for two scenarios of interest for the Hawking-Unruh effect: an inertial detector in Minkowski spacetime with an exponentially receding mirror, and an inertial detector in (1 + 1)-dimensional Schwarzschild spacetime, in the Hartle-Hawking-Israel and Unruh vacua. In the mirror spacetime the transition rate traces the onset of an energy flux from the mirror, with the expected Planckian late time asymptotics. In the Schwarzschild spacetime the transition rate of a detector that falls in from infinity gradually loses thermality, diverging near the singularity proportionally to r −3/2 .

How long does a uniformly accelerated observer need to interact with a quantum field in order to record thermality in the Unruh temperature? We address this question for a pointlike Unruh-DeWitt detector, coupled linearly to a real KleinGordon field of mass m ≥ 0 and treated within first order perturbation theory, in the limit of large detector energy gap E gap . We first show that when the interaction duration ∆T is fixed, thermality in the sense of detailed balance cannot hold as E gap → ∞, and this property generalises from the Unruh effect to any KuboMartin-Schwinger state satisfying certain technical conditions. We then specialise to a massless field in four spacetime dimensions and show that detailed balance does hold when ∆T grows as a power-law in E gap as E gap → ∞, provided the switchon and switch-off intervals are stretched proportionally to ∆T and the switching function has sufficiently strong Fourier decay. By contrast, if ∆T grows by stretching a plateau in which the interaction remains at constant strength but keeping the duration of the switch-on and switch-off intervals fixed, detailed balance at E gap → ∞ requires ∆T to grow faster than any polynomial in E gap , under mild technical conditions. These results also hold for a static detector in a Minkowski heat bath.The results limit the utility of the large E gap regime as a probe of thermality in time-dependent versions of the Hawking and Unruh effects, such as an observer falling into a radiating black hole. They may also have implications on the design of prospective experimental tests of the Unruh effect.

Abstract:We study the quantum effects of a test Klein-Gordon field in a Vaidya spacetime consisting of a collapsing null shell that forms a Schwazschild black hole, by explicitly obtaining, in a (1 + 1)-dimensional model, the Wightman function, the renormalised stress-energy tensor, and by analysing particle detector rates along stationary orbits in the exterior black hole region, and make a comparison with the folklore that the Unruh state is the state that emerges from black hole formation. In the causal future of the shell, we find a negative ingoing flux at the horizon that agrees precisely with the Unruh state calculation, and is the source of black hole radiation, while in the future null infinity we find that the radiation flux output in the Unruh state is an upper bound for the positive outgoing flux in the collapsing null shell spacetime. This indicates that back-reaction estimates based on Unruh state calculations over-estimate the energy output carried by so-called pre-Hawking radiation. The value of the output predicted by the Unruh state is however approached exponentially fast. Finally, we find that at late times, stationary observers in the exterior black hole region in the collapsing shell spacetime detect the local Hawking temperature, which is also well characterised by the Unruh state, coming from right-movers. Early-time discrepancies between the detector rates for the Unruh state and for the state in the collapsing shell spacetime are explored numerically.

We provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the GRW model. We anticipate that the collapse operators of our class of models may play a rôle in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states -a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model -supposed to be small.

We study the Fock quantization of a compound classical system consisting of point masses and a scalar field. We consider the Hamiltonian formulation of the model by using the geometric constraint algorithm of Gotay, Nester and Hinds. By relying on thisHamiltonian description, we characterize in a precise way the real Hilbert space of classical solutions to the equations of motion and use it to rigorously construct the Fock space of the system. We finally discuss the structure of this space, in particular the impossibility of writing it in a natural way as a tensor product of Hilbert spaces associated with the point masses and the field, respectively.