Unruh–DeWitt Detectors in Spherically Symmetric Dynamical Space-Times

Abstract

In the present paper, Unruh-DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh-DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein-de Sitter universe (that is a more realistic situation in the frame of ΛCDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.

Vacuum fluctuation of conformally coupled scalar field in FLRW space-times

“…In the general static case, we confirmed this result by making use of the Unruh-de Witt detector formalism [30]. In the dynamical case, the full interpretation is still missing, and one of the aims of this paper is to give a contribution in order to clarify this issue for cosmological horizons, by making use of concepts in linear quantum field theory.…”

“…This approach is similar to the one described in detail in the monograph [10] and it is the core of the adiabatic point-splitting regularization method. It is also strictly related to Unruh-De Witt detector approach (see for example [10] and references therein, and the references contained in the recent papers [30,49]). For a rigorous recent approach, see also [50].…”

“…If it does not emit as a black body one can still define a local temperature by comparing the radiation density at each point in phase space with the equilibrium Planck density, but such a local temperature will generally depend on frequency and direction. With regard to this "temperature" issue, we are particularly interested in the cosmological scenario and we would like to continue the investigation by making use of quantum field theory to evaluate the fluctuation of the simplest quantum probe at our disposal, namely a conformally coupled scalar field defined on a spherically symmetric space-time with horizons (see [29,30] and references therein).…”

Quantum Thermometers in Stationary Space-Times with Horizons

“…The probe which we are going to make use of is the simplest one and it is identified with a conformally coupled massless scalar field defined on a stationary space-time with horizon (see [22][23][24] and references therein). For a rigorous quantum theoretical approach, see also.…”

“…25 We restrict our analysis to the spherically symmetric (dynamical) case, and, in this case, the use of invariant quantities plays a crucial role. 18,19,26,23 For example, among the other things, this approach will permit the introduction of Kodama observers. For the sake of completeness, here we review the general formalism.…”