Quantum memory for Rindler supertranslations

We study the harvesting of correlations by two Unruh-DeWitt static detectors from the vacuum state of a massless scalar field in a background Vaidya spacetime consisting of a collapsing null shell that forms a Schwarzschild black hole (hereafter Vaidya spacetime for brevity), and we compare the results with those associated with the three preferred vacua (Boulware, Unruh, Hartle-Hawking-Israel vacua) of the eternal Schwarzschild black hole spacetime. To do this we make use of the explicit Wightman functions for a massless scalar field available in (1+1)-dimensional models of the collapsing spacetime and Schwarzschild spacetimes, and the detectors couple to the proper time derivative of the field. First we find that, with respect to the harvesting protocol, the Unruh vacuum agrees very well with the Vaidya vacuum near the horizon even for finite-time interactions. Second, all four vacua have different capacities for creating correlations between the detectors, with the Vaidya vacuum interpolating between the Unruh vacuum near the horizon and the Boulware vacuum far from the horizon. Third, we show that the black hole horizon inhibits any correlations, not just entanglement. Finally, we show that the efficiency of the harvesting protocol depend strongly on the signalling ability of the detectors, which is highly non-trivial in presence of curvature. We provide an asymptotic analysis of the Vaidya vacuum to clarify the relationship between the Boulware/Unruh interpolation and the near/far from horizon and early/late-time limits. We demonstrate a straightforward implementation of numerical contour integration to perform all the calculations.

Section: Resultsmentioning

confidence: 99%

Harvesting correlations in Schwarzschild and collapsing shell spacetimes

Tjoa

Mann

2020

“…Similar questions have been investigated by a number of recent studies [32][33][34][35]. Our work is mainly motivated by [33,34] where the authors studied the impact of a 'matter induced' supertranslation on the Bogoliubov coefficients between the two asymptotic states.…”

Section: Introductionmentioning

confidence: 80%

“…However, since there is no localized number operator that agrees with the global number operator for the vacuum state, the Bogoliubov coefficients are arguably not a true local observable in this context, a result deeply connected to the Reeh-Schlieder theorem, see [36][37][38][39][40][41] for further discussions. Therefore, the results obtained in [32,33,35] are global results that no localized observers can easily access. The method employed in [34] is more suitable for local calculations, since it relies on a computation of the Wightman function of the quantum field on the shockwave background, which is known to be accessible to local observers, e.g.…”

Section: Introductionmentioning

confidence: 99%

Quantum imprints of gravitational shockwaves

Gray

Kubizňák

May

et al. 2021

Gravitational shockwaves are simple exact solutions of Einstein equations representing the fields of ultrarelativistic sources and idealized gravitational waves (shocks). Historically, much work has focused on shockwaves in the context of possible black hole formation in high energy particle collisions, yet they remain at the forefront of research even today. Representing hard modes in the bulk, shocks give rise to the gravitational memory effect at the classical level and implant supertranslation (BMS) hair onto a classical spacetime at the quantum level. The aim of this paper is to further our understanding of the ‘information content’ of such supertranslations. Namely, we show that, contrary to the several claims in the literature, a gravitational shockwave does leave a quantum imprint on the vacuum state of a test quantum field and that this imprint is accessible to local observers carrying Unruh-DeWitt (UDW) detectors in this spacetime.

“…". This complements most of the literature on soft factors by focusing on bulk matter-induced supertranslation effects instead of asymptotic soft effects (for closely related work, see [33,38]). This paper is organized as follows.…”

mentioning

confidence: 76%

Invariance of Unruh and Hawking radiation under matter-induced supertranslations

Compère

Long

Riegler

2019

Matter fields are supertranslated upon crossing a shock wave, which leads to entanglement of the quantum vacuum between the two regions on either side of the shock wave. We probe this entanglement for a scalar field in a planar shock wave background by computing the Bogoliubov transformation between the inertial and uniformly accelerated observer. The resulting Bogoliubov coefficients are shown to reproduce the standard Unruh effect without dependence on the form factor of the shock wave. In contrast, excited states lead to observables that depend upon the form factor. In the context of nonspherical gravitational collapse, we comment that the angular dependence of the limiting advanced time leads to similar supertranslation effects that do not affect the Hawking spectrum but do affect scattering amplitudes.1 While a quantum completion of Einstein gravity in four-dimensional asymptotically flat spacetimes that would allow detailed computations is still far from reach, describing universal properties of Einstein gravity as a quantum low energy effective theory is possible with current techniques. The laws of black hole thermodynamics are early milestones in this endeavor, which, in particular, include Hawking's radiation and paradox [1] and the Bekenstein-Hawking area law [1][2][3]. Another universal result is the graviton dominance of high energy scattering at small deflection angles [4-8] that is described classically by a collision of shock waves [9]. Recently, a new universal property of gravity was uncovered in the infrared sector close to null infinity [10-12]: a triangular relationship exists between the displacement memory effect [13][14][15][16], the leading soft graviton theorem [17] and supertranslation asymptotic symmetries [18][19][20], see the reviews [21,22]. Displacement memory is caused by hard (i.e. finite energy) processes reaching null infinity that can be either a change of Bondi mass [13], null matter radiation [15,16] or gravitational waves [14]. Displacement memory effectively amounts to a shift of a canonical variable defined at null infinity by a supertranslation asymptotic symmetry [12]. As a result, hard processes at null infinity are accompanied by soft (i.e. infinitely low energy) processes that are mimicked by a zero energy process: a supertranslation asymptotic symmetry. This mimicking can arise because of the infrared limit taken at null infinity. In the bulk of spacetime, a supertranslation can be induced by a shock wave [23]. For planar shock waves, probes encounter a permanent displacement shift upon crossing. This has led to define the concept of soft radiation away from the infrared limit as (exactly zero energy) large diffeomorphisms (or large gauge transformations) acting in the bulk of spacetime. In particular, it led to the definition of black holes with soft hair implants . Furthermore, it has been pointed out that soft hair may bear on the black hole information paradox [12,25] and that quantum purity might be restored in principle by correlations between the hard and sof...