Remarks on distinguishability of Schwarzschild spacetime and thermal Minkowski spacetime using Resonance Casimir–Polder interaction

Abstract

The response of a single-atom detector, when placed at a point outside the horizon in Schwarzschild spacetime is the same as the response of a static single-atom detector in thermal Minkowski spacetime. So one cannot distinguish Schwarzschild spacetime from thermal Minkowski spacetime by using a single-atom detector. Here we show that beyond a characteristic length scale which is proportional to the inverse of the surface gravity κ, the Resonance Casimir-Polder interaction (RCPI) between two entangled atoms is characterized by a 1/L 2 power-law decay for the Schwarzschild spacetime when the atoms are located close to the horizon. However, the RCPI between two entangled atoms is always characterized by a 1/L power-law decay for the thermal Minkowski spacetime. These two spacetimes can be distinguished therefore using RCPI.

Qubits on the horizon: decoherence and thermalization near black holes

“…The qubit example studied here shows in detail how this can happen: the leading terms in the Nakajima-Zwanzig equation become Markovian, in the sense that ∂ t (t) depends only on (t) and not on the details of its past history prior to time t. Markovian behaviour of this form emerges for qubits near a black hole once ∆t r s (at least this is true when the redshifted energy difference ω ∞ between the two qubit energy levels -as seen by a static observer looking at the qubit far from the black hole -satisfies ω ∞ r s 1), Evolution to all orders in g 2 t is then described by a Lindblad equation [79,80]. (Some implications of Lindblad evolution in Schwarzschild geometries are also explored in [81][82][83][84][85][86][87].) By deriving the Lindblad equation as a limit of the Nakajima-Zwanzig equation for this system, we are able to assess its domain of validity.…”

“…Small σ(x, x ) should apply in particular for any two points hovering at a fixed position (r, θ, φ) = (r 0 , θ 0 , φ 0 ) just outside the Schwarzschild event horizon, with σ(x, x ) → 0 as r 0 → r s . The function σ(x, x ) is evaluated in this limit in appendix A for points on such a hovering trajectory as a function of their separation ∆t in Schwarzschild time, with the result [75,86,87])…”

Retarded resonance Casimir–Polder interaction of a uniformly rotating two-atom system

“…For a circularly rotating observer, the Planck spectrum is replaced by several ad hoc factors which impose non-thermality in the system [20]. In the RCPI, only the spontaneous radiative process occurs; hence there is no use of the number densities in the calculation of the response function [15,16,46]. Here we can write S ab jk in the form…”

“…This idea is commonly known as the thermalization theorem, which tells that if a uniformly accelerated particle detector interacts with the vacuum state of an external field and spontaneous emission occurs, then the detector behaves as if it is in a thermal bath [12]. Hence the major implementation of Casimir physics is shown in thermal-non-thermal scaling of a linearly accelerating atom, interacting with a massless scalar field [13][14][15][16]. One crucial drawback of linear accelerating detectors is that the value of the acceleration is very large if one is to produce a temperature of 1 K [17].…”

“…Benatti was first to describe the positive time-evolution of the quantum systems weakly coupled with a scalar field in the Minkowski vacuum [34]. Later, various attempts by using the QME formalism were made to analyze the Casimir physics from scratch [15,16,35]. The system-field weak coupling Hamiltonian gives an effective second-order contribution to the QME.…”