Response of an Unruh-DeWitt detector near an extremal black hole

Conroy, Aindriú; Taylor, Peter

doi:10.48550/arxiv.2109.04486

Cited by 3 publications

(11 citation statements)

References 35 publications

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“…Our techniques can be extended to more general spacetimes with horizons, such as degenerate horizons 46 , or to spacetimes in which spacetime singularities have been resolved by nonlinear effects 47 or by quantum gravity effects 48 . We leave such extensions subject to future work.…”

Section: Discussionmentioning

confidence: 99%

Quantum kicks near a Cauchy horizon

Juárez-Aubry,

Louko

2021

Preprint

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We analyse a quantum observer who falls geodesically towards the Cauchy horizon of a (1 + 1)-dimensional eternal black hole spacetime with the global structure of the non-extremal Reissner-Nordström solution. The observer interacts with a massless scalar field, using an Unruh-DeWitt detector coupled linearly to the proper time derivative of the field, and by measuring the local energy density of the field. Taking the field to be initially prepared in the Hartle-Hawking-Israel (HHI) state or the Unruh state, we find that both the detector's transition rate and the local energy density generically diverge on approaching the Cauchy horizon, respectively proportionally to the inverse and the inverse square of the proper time to the horizon, and in the Unruh state the divergences on approaching one of the branches of the Cauchy horizon are independent of the surface gravities. When the outer and inner horizons have equal surface gravities, the divergences disappear altogether in the HHI state and for one of the Cauchy horizon branches in the Unruh state. We conjecture, on grounds of comparison with the Rindler state in 1 + 1 and 3 + 1 Minkowski spacetimes, that similar properties hold in 3 + 1 dimensions for a detector coupled linearly to the quantum field, but with a logarithmic rather than inverse power-law divergence.

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Section: Discussionmentioning

confidence: 99%

Quantum kicks near a Cauchy horizon

Juárez-Aubry,

Louko

2021

Preprint

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“…In the case of a comoving observer, the KMS temperature is precisely that of the de Sitter temperature while, in the black hole case, the KMS temperature is the locally-measured Hawking temperature, Ref. [17]. Having established that a comoving detector reaches thermal equilibrium in the de Sitter universe at the limit of large detection time, we turn our attention now to finite values of detection time.…”

Section: A Comoving Detectormentioning

confidence: 98%

“…As shown in Refs. [7,17], this definition gives the expected T EDR = T loc in the limit of infinite detection time for a static detector coupled to a field in the Hartle-Hawking state, where T loc is the red-shifted Hawking temperature of the black hole. Similarly, a geodesic detector coupled to a field in the conformal vacuum of the de Sitter universe also gives the expected T EDR = T loc dS , while a comoving detector simply gives T EDR = T dS .…”

Section: Particle Detector Theorymentioning

confidence: 99%

“…[7] for a detector on a circular geodesic in Schwarzschild in the limit of infinite detection time, and in the context of the near-horizon regime of an extremal black hole in Ref. [17].…”

Section: Particle Detector Theorymentioning

confidence: 99%

“…Much work in examining the response and thermal behaviour of a detector has been carried out in the context of black holes, see for instance Refs. [7][8][9][10][11][12][13][14][15][16][17]. Here, we focus on the expanding universe so that in place of the event horizon we have the dynamical cosmological apparent horizon, and tiny fluctuations on this surface will result in the detector similarly registering low-energy radiation.…”

Section: Introductionmentioning

confidence: 99%

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Unruh-DeWitt detectors in cosmological spacetimes

Conroy

2022

Preprint

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We analyse the response and thermal behaviour of an Unruh-DeWitt detector as it travels through cosmological spacetimes, with special reference to the question of how to define surface gravity and temperature in dynamical spacetimes. Working within the quantum field theory on curved spacetime approximation, we consider a detector as it travels along geodesic and accelerated Kodama trajectories in de Sitter and asymptotically de Sitter FLRW spacetimes. By modelling the temperature of the detector using the detailed-balance form of the Kubo-Martin-Schwinger (KMS) conditions as it thermalises, we can better understand the thermal behaviour of the detector as it interacts with the quantum field, and use this to compare competing definitions of surface gravity and temperature that persist in the literature. These include the approaches of Hayward-Kodama, Ashtekar et al., Fodor et al., and Nielsen-Visser. While these are most often examined within the context of a dynamical black hole, here we shift focus to surface gravity on the evolving cosmological horizon.

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Quantum kicks near a Cauchy horizon

Juárez-Aubry

Louko

2022

AVS Quantum Science

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We analyze a quantum observer who falls geodesically toward the Cauchy horizon of a (1 þ 1)-dimensional eternal black hole spacetime with the global structure of the non-extremal Reissner-Nordstr€ om solution. The observer interacts with a massless scalar field, using an Unruh-DeWitt detector coupled linearly to the proper time derivative of the field, and by measuring the local energy density of the field. Taking the field to be initially prepared in the Hartle-Hawking-Israel (HHI) state or the Unruh state, we find that both the detector's transition rate and the local energy density generically diverge on approaching the Cauchy horizon, respectively, proportionally to the inverse and the inverse square of the proper time to the horizon, and in the Unruh state the divergences on approaching one of the branches of the Cauchy horizon are independent of the surface gravities. When the outer and inner horizons have equal surface gravities, the divergences disappear altogether in the HHI state and for one of the Cauchy horizon branches in the Unruh state. We conjecture, on grounds of comparison with the Rindler state in 1 þ 1 and 3 þ 1 Minkowski spacetimes, that similar properties hold in 3 þ 1 dimensions for a detector coupled linearly to the quantum field, but with a logarithmic rather than inverse power-law divergence.

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Response of an Unruh-DeWitt detector near an extremal black hole

Cited by 3 publications

References 35 publications

Quantum kicks near a Cauchy horizon

Quantum kicks near a Cauchy horizon

Unruh-DeWitt detectors in cosmological spacetimes

Quantum kicks near a Cauchy horizon

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