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Burgess C, Patrick S, Torres T, Gregory R, König F. Quasinormal Modes of Optical Solitons. PHYSICAL REVIEW LETTERS 2024; 132:053802. [PMID: 38364120 DOI: 10.1103/physrevlett.132.053802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 01/02/2024] [Indexed: 02/18/2024]
Abstract
Quasinormal modes (QNMs) are essential for understanding the stability and resonances of open systems, with increasing prominence in black hole physics. We present here the first study of QNMs of optical potentials. We show that solitons can support QNMs, deriving a soliton perturbation equation and giving exact analytical expressions for the QNMs of fiber solitons. We discuss the boundary conditions in this intrinsically dispersive system and identify novel signatures of dispersion. From here, we discover a new analogy with black holes and describe a regime in which the soliton is a robust black hole simulator for light-ring phenomena. Our results invite a range of applications, from the description of optical pulse propagation with QNMs to the use of state-of-the-art technology from fiber optics to address questions in black hole physics, such as QNM spectral instabilities and the role of nonlinearities in ringdown.
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Affiliation(s)
- Christopher Burgess
- School of Physics and Astronomy, SUPA, University of St. Andrews, North Haugh, St. Andrews, KY16 9SS, United Kingdom
| | - Sam Patrick
- Department of Physics, King's College London, The Strand, London, WC2R 2LS, United Kingdom
| | - Theo Torres
- Department of Physics, King's College London, The Strand, London, WC2R 2LS, United Kingdom
| | - Ruth Gregory
- Department of Physics, King's College London, The Strand, London, WC2R 2LS, United Kingdom
- Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
| | - Friedrich König
- School of Physics and Astronomy, SUPA, University of St. Andrews, North Haugh, St. Andrews, KY16 9SS, United Kingdom
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Kyutoku K, Motohashi H, Tanaka T. Quasinormal modes of Schwarzschild black holes on the real axis. Int J Clin Exp Med 2023. [DOI: 10.1103/physrevd.107.044012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
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Bargueño P, Contreras E. Minimal model for the Bekenstein-Hawking entropy. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.066001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Campos JAV, Anacleto MA, Brito FA, Passos E. Quasinormal modes and shadow of noncommutative black hole. Sci Rep 2022; 12:8516. [PMID: 35595802 PMCID: PMC9122996 DOI: 10.1038/s41598-022-12343-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 05/06/2022] [Indexed: 12/03/2022] Open
Abstract
In this paper we investigate quasinormal modes (QNM) for a scalar field around a noncommutative Schwarzschild black hole. We verify the effect of noncommutativity on quasinormal frequencies by applying two procedures widely used in the literature. The first is the Wentzel-Kramers-Brillouin (WKB) approximation up to sixth order. In the second case we use the continuous fraction method developed by Leaver. Besides, we also show that due to noncommutativity, the shadow radius is reduced when we increase the noncommutative parameter. In addition, we find that the shadow radius is nonzero even at the zero mass limit for finite noncommutative parameter.
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Affiliation(s)
- J A V Campos
- Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, Paraíba, 58051-970, Brazil
| | - M A Anacleto
- Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, Campina Grande, Paraíba, 58429-900, Brazil
| | - F A Brito
- Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, Paraíba, 58051-970, Brazil.
- Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, Campina Grande, Paraíba, 58429-900, Brazil.
| | - E Passos
- Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, Campina Grande, Paraíba, 58429-900, Brazil
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Abstract
We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with particular emphasis on the so-called μo scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the μ¯ scheme. While the jury is still out on the right scheme for black hole spacetimes, we show that as far as black hole formation is concerned, the μo scheme has another, so far unknown, serious problem. We found that in the μo scheme, no trapped surfaces would form for a nonsingular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum nonzero area of the loops over which holonomies are computed or the Barbero–Immirzi parameter decreases almost four times from its standard value. It turns out that the trapped surfaces in the μo scheme for the marginally bound case are also forbidden for an arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We found that in contrast to the situation in the μo scheme, black holes can form in the μ¯ scheme, as well as other lattice refinements with a mass gap determined by quantum geometry.
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Chatterjee A, Ghosh A. Exponential Corrections to Black Hole Entropy. PHYSICAL REVIEW LETTERS 2020; 125:041302. [PMID: 32794826 DOI: 10.1103/physrevlett.125.041302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Revised: 03/07/2020] [Accepted: 06/23/2020] [Indexed: 06/11/2023]
Abstract
Using the quasilocal properties alone we show that the area spectrum of a black hole horizon must be discrete, independent of any specific quantum theory of gravity. The area spectrum is found to be half-integer spaced with values 8πγℓ_{p}^{2}j where j∈N/2. We argue that if microstate counting is carried out for quantum states residing on the horizon only, correction of exp(-A/4ℓ_{p}^{2}) over the Bekenstein-Hawking area law must arise in black hole entropy.
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Affiliation(s)
- Ayan Chatterjee
- Department of Physics and Astronomical Science, Central University of Himachal Pradesh, Dharamshala 176215, India
| | - Amit Ghosh
- Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India and Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India
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Coates A, Völkel SH, Kokkotas KD. Spectral Lines of Quantized, Spinning Black Holes and their Astrophysical Relevance. PHYSICAL REVIEW LETTERS 2019; 123:171104. [PMID: 31702264 DOI: 10.1103/physrevlett.123.171104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2019] [Revised: 07/30/2019] [Indexed: 06/10/2023]
Abstract
In this Letter, we study black hole area quantization in the context of gravitational wave physics. It was recently argued that black hole area quantization could be a mechanism to produce so-called echoes as well as characteristic absorption lines in gravitational wave observations of merging black holes. One can match the spontaneous decay of these quantum black holes to Hawking radiation calculations. Using some assumptions, one can then estimate the natural widths of these states. As can be seen from a classical paper by Bekenstein and Mukhanov, the ratio between width and spacing of nonspinning black hole states approaches a small constant, which seems to confirm the claim. However, we find that, including the effect of black hole spin, the natural widths increase. To properly address any claim about astrophysical black holes, one should examine the spinning case, as real black holes spin. Thus, the word "spinning" is key to the question of whether or not black holes should have an observable spectrum in nature. Our results suggest that it should be possible to distinguish between any scenarios for which the answer to this question is yes. However, for all of the commonly discussed scenarios, our answer is "almost certainly no."
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Affiliation(s)
- Andrew Coates
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
| | - Sebastian H Völkel
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
| | - Kostas D Kokkotas
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
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Perez A. Black holes in loop quantum gravity. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:126901. [PMID: 28696338 DOI: 10.1088/1361-6633/aa7e14] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This is a review of results on black hole physics in the context of loop quantum gravity. The key feature underlying these results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum gravity. Quantum discreteness follows directly from the canonical quantization prescription when applied to the action of general relativity that is suitable for the coupling of gravity with gauge fields, and especially with fermions. Planckian discreteness and causal considerations provide the basic structure for the understanding of the thermal properties of black holes close to equilibrium. Discreteness also provides a fresh new look at more (at the moment) speculative issues, such as those concerning the fate of information in black hole evaporation. The hypothesis of discreteness leads, also, to interesting phenomenology with possible observational consequences. The theory of loop quantum gravity is a developing program; this review reports its achievements and open questions in a pedagogical manner, with an emphasis on quantum aspects of black hole physics.
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Affiliation(s)
- Alejandro Perez
- Centre de Physique Théorique, Aix Marseille Universit, Universit de Toulon, CNRS, UMR 7332, 13288 Marseille, France
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Panza N, Rodrigues H, Cocuroci D, Helayël-Neto J. Discussion on possible effects of the Barbero-Immirzi parameter at the TeV-scale particle physics. Int J Clin Exp Med 2014. [DOI: 10.1103/physrevd.90.125007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Zhou XN, Du XL, Yang K, Liu YX. Dirac dynamical resonance states around Schwarzschild black holes. Int J Clin Exp Med 2014. [DOI: 10.1103/physrevd.89.043006] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chen S, Jing J. Dynamical evolution of the electromagnetic perturbation with Weyl corrections. Int J Clin Exp Med 2013. [DOI: 10.1103/physrevd.88.064058] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Casals M, Ottewill A. Spectroscopy of the Schwarzschild black hole at arbitrary frequencies. PHYSICAL REVIEW LETTERS 2012; 109:111101. [PMID: 23005609 DOI: 10.1103/physrevlett.109.111101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2012] [Indexed: 06/01/2023]
Abstract
Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.
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Affiliation(s)
- Marc Casals
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5.
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Wei SW, Liu YX, Yang K, Zhong Y. Entropy/area spectra of the charged black hole from quasinormal modes. Int J Clin Exp Med 2010. [DOI: 10.1103/physrevd.81.104042] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Fernando S. Spinning dilaton black holes in2+1dimensions: Quasinormal modes and the area spectrum. Int J Clin Exp Med 2009. [DOI: 10.1103/physrevd.79.124026] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Maggiore M. Physical interpretation of the spectrum of black hole quasinormal modes. PHYSICAL REVIEW LETTERS 2008; 100:141301. [PMID: 18518020 DOI: 10.1103/physrevlett.100.141301] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2007] [Indexed: 05/26/2023]
Abstract
When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies omega=omega R +i omega I. We show that this behavior is the same as that of damped harmonic oscillators whose real frequencies are (omega R2+omega I 2)1/2, rather than simply omega R. Since, for highly excited modes, omega I>>omega R, this observation changes drastically the physical understanding of the black hole spectrum and forces a reexamination of various results in the literature. In particular, adapting a derivation by Hod, we find that the area of the horizon of a Schwarzschild black hole is quantized in units Delta A=8pi l Pl2, in contrast with the original result Delta A=4log(3)l Pl2.
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Affiliation(s)
- Michele Maggiore
- Département de Physique Théorique, Université de Genève, 24 quai Ansermet, CH-1211 Genève 4, Switzerland
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Corichi A, Díaz-Polo J, Fernández-Borja E. Black hole entropy quantization. PHYSICAL REVIEW LETTERS 2007; 98:181301. [PMID: 17501557 DOI: 10.1103/physrevlett.98.181301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2006] [Indexed: 05/15/2023]
Abstract
Ever since the pioneering works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that the black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is not quantized in equidistant steps, can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show consistency with the Bekenstein framework when an oscillatory behavior in the entropy-area relation is properly interpreted.
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Affiliation(s)
- Alejandro Corichi
- Instituto de Matemáticas, Unidad Morelia, Universidad Nacional Autónoma de México, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacán 58090, Mexico.
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Cho HT. Asymptotic quasinormal frequencies of different spin fields in spherically symmetric black holes. Int J Clin Exp Med 2006. [DOI: 10.1103/physrevd.73.024019] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Castello-Branco KC, Konoplya RA, Zhidenko A. High overtones of Dirac perturbations of a Schwarzschild black hole. Int J Clin Exp Med 2005. [DOI: 10.1103/physrevd.71.047502] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Pinamonti N, Vanzo L. Central charges and boundary fields for two-dimensional dilatonic black holes. Int J Clin Exp Med 2004. [DOI: 10.1103/physrevd.69.084012] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Birmingham D, Carlip S. Nonquasinormal modes and black hole physics. PHYSICAL REVIEW LETTERS 2004; 92:111302. [PMID: 15089123 DOI: 10.1103/physrevlett.92.111302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2003] [Indexed: 05/24/2023]
Abstract
The near-horizon geometry of a large class of extremal and near-extremal black holes in string and M-theory contains three-dimensional asymptotically anti-de Sitter space. Motivated by this structure, we are led naturally to a discrete set of complex frequencies defined in terms of the monodromy at the inner and outer horizons of the black hole. We show that the correspondence principle, whereby the real part of these "nonquasinormal frequencies" is identified with certain fundamental quanta, leads directly to the correct quantum behavior of the near-horizon Virasoro algebra, and thus the black hole entropy. Remarkably, for the rotating black hole in five dimensions we also reproduce the fractionization of conformal weights predicted in string theory.
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Affiliation(s)
- Danny Birmingham
- Department of Physics, University of California, Davis, California 95616, USA.
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