Quantum stress tensor at the Cauchy horizon of Reissner-Nordström-deSitter spacetime

Hollands, Stefan; Klein, Christiane; Zahn, Jochen

doi:10.48550/arxiv.2006.10991

Cited by 3 publications

(6 citation statements)

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“…That horizons with equal surface gravities emerge as the exceptionally regular special case may not be surprising: that this case is special was already known from consideration of the stress-energy tensor [15][16][17] , and similar observations arise with 'lukewarm' black holes, in which two Killing horizons bound a spacetime region in which the Killing vector in question is timelike 42,43 . It is however notable that in the HHI state, the overall sign of the leading divergence is determined by which of the two surface gravities is greater, in precisely the same way for both the detector's transition rate and for the energy density seen by an observer.…”

Section: Discussionmentioning

confidence: 79%

“…Changing variables in (A. 16) by τ = τ − s gives I(ω, τ, τ 0 ) = I 1 (ω, τ, τ 0 ) + I 2 (ω, τ, τ 0 ), (A.17a)…”

Section: First Boundary Term In (V2)mentioning

confidence: 99%

“…When the theory is extended to include quantised fields, new issues arise from the renormalised stressenergy tensor near the Cauchy horizon, and from the back-reaction of this stress-energy on the spacetime. There is evidence that the back-reaction of the quantum fields tends to make Cauchy horizons generically unstable even in situations where classical surface gravity considerations would suggest stability [13][14][15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

“…The main difference is that the energy density generically diverges proportionally to the inverse square, rather than the inverse, of the proper time separation from the Cauchy horizon; however, in the energy density averaged over the trajectory, the divergence is again proportional to the inverse of the proper time separation from the Cauchy horizon. The divergence in the stress-energy tensor, including the special role of the equal surface gravity case therein, has been studied in the context of back-reaction, in both 1 + 1 dimensions and in 3 + 1 dimensions [15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

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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: 79%

“…Changing variables in (A. 16) by τ = τ − s gives I(ω, τ, τ 0 ) = I 1 (ω, τ, τ 0 ) + I 2 (ω, τ, τ 0 ), (A.17a)…”

Section: First Boundary Term In (V2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum kicks near a Cauchy horizon

Juárez-Aubry,

Louko

2021

Preprint

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“…Thus, the question of the validity of Conjecture 4 becomes even more subtle for Λ > 0 and has received lots of attention in the recent literature. We refer to the conjecture in [16], the survey article [91], the recent results [21,24,23,22,12] and the works [51,50] taking also quantum effects into account.…”

Section: Strong Cosmic Censorship: Conjectures 1-4mentioning

confidence: 99%

Diophantine approximation as Cosmic Censor for Kerr-AdS black holes

Kehle¹

2020

Preprint

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The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior of waves on black hole interiors with negative cosmological constant Λ < 0 and explore the consequences of this for the Strong Cosmic Censorship conjecture in general relativity.We study linear scalar perturbations ψ of Kerr-AdS solving g ψ− 2 3 Λψ = 0 with reflecting boundary conditions imposed at infinity. Understanding the behavior of ψ at the Cauchy horizon corresponds to a linear analog of the problem of Strong Cosmic Censorship. Our main result shows that if the dimensionless black hole parameters mass m = M √ −Λ and angular momentum a = a √ −Λ satisfy a certain non-Diophantine condition, then perturbations ψ arising from generic smooth initial data blow up |ψ| → +∞ at the Cauchy horizon. The proof crucially relies on a novel resonance phenomenon between stable trapping on the black hole exterior and the poles of the interior scattering operator that gives rise to a small divisors problem. Our result is in stark contrast to the result on Reissner-Nordström-AdS [61] as well as to previous work on the analogous problem for Λ ≥ 0-in both cases such linear scalar perturbations were shown to remain bounded.As a result of the non-Diophantine condition, the set of parameters m, a for which we show blow-up forms a Baire-generic but Lebesgue-exceptional subset of all parameters below the Hawking-Reall bound. On the other hand, we conjecture that for a set of parameters m, a which is Baire-exceptional but Lebesgue-generic, all linear scalar perturbations remain bounded at the Cauchy horizon |ψ| ≤ C. This suggests that the validity of the C 0 -formulation of Strong Cosmic Censorship for Λ < 0 may change in a spectacular way according to the notion of genericity imposed.

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On the initial value problem for semiclassical gravity without and with quantum state collapses

Juárez-Aubry¹,

Kay²,

Miramontes³

et al. 2022

Preprint

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Semiclassical gravity is the theory in which the classical Einstein tensor of a spacetime is coupled to quantum matter fields propagating on the spacetime via the expectation value of their renormalized stress-energy tensor in a quantum state. We explore two issues, taking the Klein Gordon equation as our model quantum field theory. The first is the provision of a suitable initial value formulation for the theory. Towards this, we address the question, for given initial data consisting of the classical metric and its first three 'time' derivatives off the surface together with a choice of initial quantum state, of what is an appropriate 'surface Hadamard' condition such that, when the relevant constraint equations hold too, it is reasonable to conjecture that there will be a Cauchy development whose quantum state is Hadamard. This requires dealing with the fact, that given two points on an initial surface, the spacetime geodesic between them does not, in general, lie in that surface. So the geodesic distance that occurs in the Hadamard subtraction differs from the geodesic distance intrinsic to the initial surface. We handle this complication with a suitable 3dimensional covariant Taylor expansion. Moreover the renormalized expectation value of the stress-energy tensor in the initial surface depends explicitly on the fourth 'time' derivative of the metric, which is not part of the initial data, but which we argue is given, implicitly, by the semiclassical Einstein equations on the initial surface. We also introduce the notion of physical solutions, which, inspired by a 1993 proposal of Parker and Simon, we define to be solutions which are smooth in at = 0 -and conjecture that, for these, the second and third time derivatives of the metric will be determined by the remaining initial data. Finally we point out that a simpler treatment of the initial value problem can be had if we adopt yet more of the spirit of Parker and Simon and content ourselves with solutions to order which are Hadamard to order . A further simplification occurs if we consider semiclassical gravity to order 0 . This resembles classical general relativity in that it is free from the complications of higher derivative terms and does not require any Hadamard condition. But it can still incorporate nontrivial quantum features such as superpositions of classical-like quantum states of the matter fields. Our second issue concerns the prospects

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Quantum stress tensor at the Cauchy horizon of Reissner-Nordström-deSitter spacetime

Cited by 3 publications

References 0 publications

Quantum kicks near a Cauchy horizon

Quantum kicks near a Cauchy horizon

Diophantine approximation as Cosmic Censor for Kerr-AdS black holes

On the initial value problem for semiclassical gravity without and with quantum state collapses

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