Quantum stress tensor in the three-dimensional black hole

Steif, Alan R.

doi:10.1103/physrevd.49.r585

Cited by 96 publications

(192 citation statements)

References 31 publications

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“…As well as their classical properties, the behaviour of quantum fields on the BTZ black hole has been extensively studied (see, for example, [7,8,9,10]). One advantage of working in three dimensions is that many of the computational aspects are greatly simplified (for example, it is possible to write the Green's function for a quantum field in the Hartle-Hawking state in closed form [11,12,13]). However, there has been more recent interest in higher-dimensional black holes in anti-de Sitter space, particularly Kerr-Newman-anti-de Sitter (KN-AdS) black holes in various dimensions [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Classical super-radiance in Kerr–Newman–anti-de Sitter black holes

Winstanley¹

2001

Phys. Rev. D

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We study in detail the modes of a classical scalar field on a KerrNewman-anti-de Sitter (KN-AdS) black hole. We construct sets of basis modes appropriate to the two possible boundary conditions ("reflective" and "transparent") at time-like infinity, and consider whether super-radiance is possible. If we employ "reflective" boundary conditions, all modes are non-super-radiant. On the other hand, for "transparent" boundary conditions, the presence of super-radiance depends on our definition of positive frequency. For those KN-AdS black holes having a globally time-like Killing vector, the natural choice of positive frequency leads to no super-radiance. For other KN-AdS black holes, there is a choice of positive frequency which gives no super-radiance, but for other choices there will, in general, be super-radiance.

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Section: Introductionmentioning

confidence: 99%

Classical super-radiance in Kerr–Newman–anti-de Sitter black holes

Winstanley¹

2001

Phys. Rev. D

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“…A similar computation in the BTZ case, namely M > 0, yields the same result, but with 10) in place of C n , where ln N = 2πr + , and on the diagonal…”

Section: The Vacuum Expectation Value Of the Stress Tensormentioning

confidence: 48%

“…the BTZ solution in the limit of a vanishing black hole mass), generalizing to the nonconformally invariant case previous results obtained in [9][10][11][12][13][14]. We shall also attempt to explore the possible relevance of the quantum fluctuations with regard to the issue of the cosmic censorship hipothesys, since the BTZ ground state solution shows a naked singularity and, presumably, it might be the final state at the end of the black-hole evaporation process.…”

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confidence: 99%

Quantum scalar field on the massless(2+1)-dimensional black hole background

Binosi¹,

Moretti

Vanzo

et al. 1999

Phys. Rev. D

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The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Bañados, Teitelboim and Zanelli which contains a naked singularity. The one-loop BTZ partition function and the associate black hole effective entropy, the expectation value of the quantum fluctuation as well as the renormalized expectation value of the stress tensor are explicitly computed in the framework of the ζ-function procedure. This is done for all values of the coupling with the curvature, the mass of the field and the temperature of the quantum state. In the massless conformally coupled case, the found stress tensor is used for determining the quantum back reaction on the metric due to the scalar field in the quantum vacuum state, by solving the semiclassical Einstein equations. It is finally argued that, within the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is implemented since the naked singularity of the ground state metric is shielded by an event horizon created by the back reaction.

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“…The smoothness of the quotient geometry is also deceptive, and the singularity well deserves its name once one makes any attempt to physically probe it. After quotienting the lightcones of figure 3, they are comprised of closed lightlike curves where even small (quantum) fluctuations [38,39] can backreact divergently with divergent curvatures, and general considerations imply the breakdown of ordinary (effective) field theory [40]. See [41] for a concise review of these general considerations.…”

Section: Through the Singularity: The "Whisker" Regionsmentioning

confidence: 99%

“…See [41] for a concise review, and [38,39] for computations of stress-tensor divergences at the BTZ singularity. Similar features have also been studied in string theory (as reviewed in [42].)…”

Section: Jhep09(2014)073mentioning

confidence: 99%

Holography of the BTZ black hole, inside and out

Fuente

Sundrum

2014

J. High Energ. Phys.

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We propose a 1 + 1 dimensional CFT dual structure for quantum gravity and matter on the extended 2 + 1 dimensional BTZ black hole, realized as a quotient of the Poincaré patch of AdS 3 . The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincaré patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.

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Quantum stress tensor in the three-dimensional black hole

Cited by 96 publications

References 31 publications

Classical super-radiance in Kerr–Newman–anti-de Sitter black holes

Classical super-radiance in Kerr–Newman–anti-de Sitter black holes

Quantum scalar field on the massless(2+1)-dimensional black hole background

Holography of the BTZ black hole, inside and out

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