Bohr's Correspondence Principle and the Area Spectrum of Quantum Black Holes

Hod, Shahar

doi:10.1103/physrevlett.81.4293

Cited by 666 publications

(1,091 citation statements)

References 21 publications

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“…In a remarkable paper [3], York proposed the intriguing idea to model the quantum BH in terms of BH QNMs. More recently, by using Bohr's Correspondence Principle, Hod proposed that QNMs should release information about the area quantization as QNMs are associated to absorption of particles [4,5]. Hod's work was improved by Maggiore [6] who solved some important problems.…”

Section: Introductionmentioning

confidence: 99%

“…Hod was the first author to note that the constant (2) can be written in terms of ln 3 and proposed an intriguing interpretation in order to explain this fact [4,5], as we will see below. On the other hand, the imaginary part of (1) can be easily understood [2].…”

Section: Hod's Original Proposalmentioning

confidence: 99%

“…In a famous paper, Bekenstein [15] showed that the area quantum of the Schwarzschild BH is △A = 8π (we recall that the Planck distance l p = 1.616 × 10 −33 cm is equal to one in Planck units). Using properties of the spectrum of Schwarzschild BH QNMs a different numerical coefficient has been found by Hod in [4,5]. Hod's analysis started by observing that, as for the Schwarzschild BH the horizon area A is related to the mass through the relation A = 16πM 2 , a variation △M in the mass generates a variation…”

Section: Hod's Original Proposalmentioning

confidence: 99%

“…For Schwarzschild BH and in strictly thermal approximation, QNMs are usually labelled as ω nl , where n and l are the "overtone" and the angular momentum quantum numbers [1,2,4,5,6]. For each l≥ 2 for BH perturbations, we have a countable infinity of QNMs, labelled by n (n = 1, 2, ...) [1,2,4,5,6].…”

Section: Hod's Original Proposalmentioning

confidence: 99%

“…For each l≥ 2 for BH perturbations, we have a countable infinity of QNMs, labelled by n (n = 1, 2, ...) [1,2,4,5,6]. Working with G = c = k B = = 1 4πǫ0 = 1 (Planck units), for large n BH QNMs become independent of l having the structure [1,2,4,5,6] …”

Section: Hod's Original Proposalmentioning

confidence: 99%

See 4 more Smart Citations

On Quasi-Normal Modes, Area Quantization and Bohr Correspondence Principle

Corda

2015

Int J Theor Phys

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In Int. Journ. Mod. Phys. D 14, 181 (2005), the author Khriplovich verbatim claims that "the correspondence principle does not dictate any relation between the asymptotics of quasinormal modes and the spectrum of quantized black holes" and that "this belief is in conflict with simple physical arguments". In this paper we analyze Khriplovich's criticisms and realize that they work only for the original proposal by Hod, while they do not work for the improvements suggested by Maggiore and recently finalized by the author and collaborators through a connection between Hawking radiation and black hole (BH) quasi-normal modes (QNMs). This is a model of quantum BH somewhat similar to the historical semiclassical model of the structure of a hydrogen atom introduced by Bohr in 1913. Thus, QNMs can be really interpreted as BH quantum levels (the "electrons" of the "Bohr-like BH model").Our results have also important implications on the BH information puzzle.

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Section: Introductionmentioning

confidence: 99%

Section: Hod's Original Proposalmentioning

confidence: 99%

Section: Hod's Original Proposalmentioning

confidence: 99%

Section: Hod's Original Proposalmentioning

confidence: 99%

Section: Hod's Original Proposalmentioning

confidence: 99%

See 3 more Smart Citations

On Quasi-Normal Modes, Area Quantization and Bohr Correspondence Principle

Corda

2015

Int J Theor Phys

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Spectroscopy of rotating linear dilaton black holes from boxed quasinormal modes

Сакалли

Tokgöz

2016

Annalen der Physik

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Numerical studies of the coupled Einstein-Klein-Gordon system have recently revealed that confined scalar fields generically collapse to form caged black holes. In the light of this finding, we analytically study the characteristic resonance spectra of the confined scalar fields in rotating linear dilaton black hole geometry. Confining mirrors (cage) are assumed to be placed in the near-horizon region of a caged rotating linear dilaton black hole rm−r 2 r 2 ≪ 1 (rm is the radius of the cage and r2 represents the event horizon). The radial part of the Klein-Gordon equation is written as a Schrödinger-like wave equation, which reduces to a Bessel differential equation around the event horizon. Using analytical tools and proper boundary conditions, we obtain the boxed-quasinormal mode frequencies of the caged rotating linear dilaton black hole. Finally, we employ Maggiore's method, which evaluates the transition frequency in the adiabatic invariant quantity from the highly damped quasinormal modes, in order to investigate the entropy/area spectra of the rotating linear dilaton black hole.

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Quasinormal modes of BTZ black hole and Hawking‐like radiation in graphene

Kandemir

Ertem

2017

Annalen der Physik

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The Bañados-Teitelboim-Zanelli (BTZ) black hole model corresponds to a solution of (2+1)-dimensional Einstein gravity with negative cosmological constant, and by a conformal rescaling its metric can be mapped onto the hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature. Beltrami trumpet shaped graphene sheets have been predicted to emit Hawking radiation that is experimentally detectable by a scanning tunnelling microscope. Here, for the first time we present an analytical algorithm that allows variational solutions to the Dirac Hamiltonian of graphene pseudoparticles in BTZ black hole gravitational field by using an approach based on the formalism of pseudo-Hermitian Hamiltonians within a discrete-basis-set method. We show that our model not only reproduces the exact results for the real part of quasinormal mode frequencies of (2+1)-dimensional spinless BTZ black hole, but also provides analytical results for the real part of quasinormal modes of spinning BTZ black hole, and also offers some predictions for the observable effects with a view to gravity-like phenomena in a curved graphene sheet.PACS numbers: 04.62.+v, 72.80.Vp,04.70.Dy After the work of Unruh[1] who first pointed out that quantum fluid systems can be used to create an analogue of a black hole in the laboratory, various analogue gravity systems from superfluid 3 He to ultracold fermions (see e.g. [2]) have been proposed to mimic the Hawking radiation emitted by a black hole. Recently, in a series of papers [3][4][5][6][7] Iorio and Lambiase proposed a Beltrami trumpet shaped graphene as a tabletop experiment for the quantum simulation of a black hole, i.e., an analogue black hole to detect the Hawking-Unruh radiation by a scanning tunneling microscope (STM). The Beltami trumpet shaped graphene can be thought as a deformed graphene that have been wrapped up into a hyperbolic pseudosphere with a constant negative curvature.(2+1)-dimensional (3D) BTZ black hole model[8] with a negative cosmological constant Λ = −1/l 2 exhibits similar thermodynamical properties to those of (3+1)-dimensional Kerr black holes due to having mass (M), angular momentum (J), and inner and outer horizons. Since it was shown by Cvetič and Gibbons [9] that the metric of the BTZ black hole can be mapped onto the Beltrami trumpet, studying the low energy excitations of Dirac pseudoparticles in a Beltrami trumpet shaped graphene surface allows one to study quantum properties of the event horizon and Hawking-like radiation within the BTZ black hole background. The details of this proposal and its implications are discussed in a comprehensive paper of Iorio and Lambiase [7].On the gravity side, the first exact solution of quasinormal modes and associated frequencies for 3D spinless BTZ model were obtained by Cardoso and Lemos [10] and subsequently by Birmingham[11], and to our knowledge no exact or rigorous solutions for quasinormal modes are available for 3D spinning BTZ black hole. It is well known that, instead of normal modes, one should deal with qu...

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Bohr's Correspondence Principle and the Area Spectrum of Quantum Black Holes

Cited by 666 publications

References 21 publications

On Quasi-Normal Modes, Area Quantization and Bohr Correspondence Principle

On Quasi-Normal Modes, Area Quantization and Bohr Correspondence Principle

Spectroscopy of rotating linear dilaton black holes from boxed quasinormal modes

Quasinormal modes of BTZ black hole and Hawking‐like radiation in graphene

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