scholarly journals Spectral Problems for Quasinormal Modes of Black Holes

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 476
Author(s):  
Yasuyuki Hatsuda ◽  
Masashi Kimura
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Quasinormal Modes ◽  
Review Article ◽  
Wkb Method ◽  
Spectral Problems ◽  
Points Of View ◽  
Numerical Treatments

This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes analytical/numerical treatments, semiclassical perturbation theory, the (uniform) WKB method and useful mathematical tools: Borel summations, Padé approximants, and so forth. The article is not comprehensive, but rather looks into a few examples from various points of view. The techniques in this article are widely applicable to many other examples.

scholarly journals Greybody factor and quasinormal modes of Regular Black Holes

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Ángel Rincón ◽  
Victor Santos
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Classical Solution ◽  
Quantum Number ◽  
Quasinormal Modes ◽  
Wkb Method ◽  
Regular Black Hole ◽  
Gravitational Perturbations ◽  
Black Hole Solutions

AbstractIn this work, we investigate the quasinormal frequencies of a class of regular black hole solutions which generalize Bardeen and Hayward spacetimes. In particular, we analyze scalar, vector and gravitational perturbations of the black hole with the semianalytic WKB method. We analyze in detail the behaviour of the spectrum depending on the parameter p/q of the black hole, the quantum number of angular momentum and the s number. In addition, we compare our results with the classical solution valid for $$p = q = 1$$ p = q = 1 .

scholarly journals Black Hole Quasinormal Modes and Seiberg–Witten Theory

2021 ◽  
Author(s):  
Gleb Aminov ◽  
Alba Grassi ◽  
Yasuyuki Hatsuda
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Perturbation Theory ◽  
Partition Function ◽  
Gauge Theories ◽  
Quasinormal Modes ◽  
Spheroidal Harmonics ◽  
Witten Theory ◽  
Supersymmetric Gauge ◽  
Exact Version

AbstractWe present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $${\mathcal {N}}=2$$ N = 2 supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the $$\Omega $$ Ω -background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.

scholarly journals A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method

2012 ◽  
Vol 2012 ◽  
pp. 1-42 ◽  
Author(s):  
H. T. Cho ◽  
A. S. Cornell ◽  
Jason Doukas ◽  
T.-R. Huang ◽  
Wade Naylor
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Iteration Method ◽  
Quasinormal Modes ◽  
Kerr Black Hole ◽  
Asymptotic Iteration Method ◽  
Wkb Method ◽  
New Approach ◽  
Higher Dimensional ◽  
First Time

We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. We demonstrate that the AIM can be used to find radial QNMs for Schwarzschild, Reissner-Nordström (RN), and Kerr black holes in a unified way. We discuss some advantages of the AIM over the continued fractions method (CFM). This paper presents for the first time the spin 0, 1/2 and 2 QNMs of a Kerr black hole and the gravitational and electromagnetic QNMs of the RN black hole calculated via the AIM and confirms results previously obtained using the CFM. We also present some new results comparing the AIM to the WKB method. Finally we emphasize that the AIM is well suited to higher-dimensional generalizations and we give an example of doubly rotating black holes.

QUANTIZATION OF ENTROPY SPECTRA OF BLACK HOLES

2013 ◽  
Vol 22 (02) ◽  
pp. 1330001 ◽  
Author(s):  
YONGJOON KWON ◽  
SOONKEON NAM
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Correspondence Principle ◽  
Scattering Problem ◽  
Classical System ◽  
Quasinormal Modes ◽  
Entropy Spectrum ◽  
Total Transmission ◽  
Transmission Modes ◽  
Characteristic Modes

From the quasinormal modes (QNM) of black holes, we obtain the quantizations of the entropy and horizon area of black holes via Bohr–Sommerfeld quantization, based on Bohr's correspondence principle. For this, we identify the appropriate action variable of the classical system corresponding to a black hole. By considering the BTZ black holes in topologically massive gravity as well as Einstein gravity, it is found that the spectra of not the horizon areas but the entropies of black holes are equally spaced. We also propose that other characteristic modes of black holes, which are non-QNM or holographic QNM, can be used in quantization of entropy spectra just like QNM. From these modes, it is found that only the entropy spectrum of the warped AdS3 black hole is equally spaced as well. Furthermore, by considering a scattering problem in a black hole, we propose that the total transmission modes and total reflection modes of black holes can be regarded as characteristic modes of black holes and result in the equally spaced entropy of the Kerr and Reissner–Nordström black holes. Finally, we conclude that there is a universal behavior that the entropy spectra of various black holes are equally spaced.

Frontiers of Quantum Black Holes

2020 ◽  
Vol 29 (11) ◽  
pp. 10-16
Author(s):  
Wontae KIM ◽  
Mu-In PARK
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Direct Detection ◽  
Occupation Number ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Quantum Radiation ◽  
Points Of View ◽  
Massless Quantum

A black hole is a theoretical prediction of Einstein’s general theory of relativity, differently from Newtonian gravity, which is a non-relativistic gravity. In recent few years, its direct detection via gravitational waves and other multi-messenger observations have made it possible to test the prediction and hence its associated general relativity. From purely theoretical points of view, general relativity cannot be a complete description due to its not being compatible with quantum mechanics, which is a successful description of microscopic objects. In this article, we introduce the conceptional development of quantum-gravity theories and give brief sketches of fundamental problems in quantum black holes. As an interesting model of quantum black holes, we consider a collapsing shell of matter to form a Hayward black hole and investigate semiclassically quantum radiation from the shell. By using the Israel’s formulation and the functional Schrödinger formulation for massless quantum radiation, we find that the Hawking temperature can be deduced from the occupation number of excited states when the shell approaches its own horizon.

scholarly journals Deforming charged black holes with dipolar differential rotation boundary

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Tong-Tong Hu ◽  
Shuo Sun ◽  
Hong-Bo Li ◽  
Yong-Qiang Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Chemical Potential ◽  
Dimensional Space ◽  
Quasinormal Modes ◽  
Fixed Temperature ◽  
First Case ◽  
Ads Black Holes ◽  
Horizon Geometry ◽  
Black Hole Solutions

Abstract Motivated by the recent studies of the novel asymptotically global $$\hbox {AdS}_4$$AdS4 black hole with deformed horizon, we consider the action of Einstein–Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge q and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. The entropy and quasinormal modes of deforming charged AdS black hole are also studied in this paper. Due to the existence of charge q, the phase diagram of entropy is more complicated. We consider two cases of solutions: (1) fixing the chemical potential $$\mu $$μ; (2) changing the value of $$\mu $$μ according to the values of horizon radius and charge. In the first case, it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature, but these two black holes have same horizon geometry and entropy. The second case ensures that deforming charged AdS black hole solutions can reduce to standard RN–AdS black holes.

scholarly journals Quasinormal modes and van der Waals-like phase transition of charged AdS black holes in Lorentz symmetry breaking massive gravity

2019 ◽  
Vol 28 (09) ◽  
pp. 1950113 ◽  
Author(s):  
Bin Liang ◽  
Shao-Wen Wei ◽  
Yu-Xiao Liu
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Symmetry Breaking ◽  
Quasinormal Modes ◽  
Massive Gravity ◽  
Quasinormal Mode ◽  
Large Black Hole ◽  
Sign Change ◽  
Lorentz Symmetry Breaking

Using the quasinormal modes of a massless scalar perturbation, we investigate the small/large black hole phase transition in the Lorentz symmetry breaking massive gravity. We mainly focus on two issues: (i) the sign change of slope of the quasinormal mode frequencies in the complex-[Formula: see text] diagram; (ii) the behaviors of the imaginary part of the quasinormal mode frequencies along the isobaric or isothermal processes. For the first issue, our result shows that, at low fixed temperature or pressure, the phase transition can be probed by the sign change of slope. While increasing the temperature or pressure to certain values near the critical point, there will appear the deflection point, which indicates that such method may not be appropriate to test the phase transition. In particular, the behavior of the quasinormal mode frequencies for the small and large black holes tend to be the same at the critical point. For the second issue, it is shown that the nonmonotonic behavior is observed only when the small/large black hole phase transition occurs. Therefore, this property can provide us with an additional method to probe the phase transition through the quasinormal modes.

scholarly journals QUASINORMAL MODES AND LATE-TIME TAILS OF CANONICAL ACOUSTIC BLACK HOLES

2007 ◽  
Vol 16 (07) ◽  
pp. 1211-1218 ◽  
Author(s):  
PING XI ◽  
XIN-ZHOU LI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Wave Propagation ◽  
Angular Momentum ◽  
Numerical Method ◽  
Time Scale ◽  
Quasinormal Modes ◽  
Late Time ◽  
Classical Wave ◽  
Acoustic Black Holes

In this paper, we investigate the evolution of classical wave propagation in the canonical acoustic black hole by a numerical method and discuss the details of the tail phenomenon. The oscillating frequency and damping time scale both increase with the angular momentum l. For lower l, numerical results show the lowest WKB approximation gives the most reliable result. We also find that the time scale of the interim region from ringing to tail is not affected obviously by changing l.

scholarly journals QUASINORMAL MODES OF CHARGED DILATON BLACK HOLES AND THEIR ENTROPY SPECTRA

2013 ◽  
Vol 28 (27) ◽  
pp. 1350109 ◽  
Author(s):  
I. SAKALLI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quasinormal Modes ◽  
Energy Limit ◽  
Small Perturbations ◽  
Asymptotically Flat ◽  
Dimensionless Constant ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole ◽  
Dilaton Black Hole

In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter a, it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNM in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these black holes (BHs). Although the QNM frequencies are tuned by a, we show that the quantum spectra do not depend on a, and they are equally spaced. On the other hand, the obtained value of undetermined dimensionless constant ϵ is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.

scholarly journals AREA SPECTRUM OF KERR AND EXTREMAL KERR BLACK HOLES FROM QUASINORMAL MODES

2005 ◽  
Vol 20 (25) ◽  
pp. 1923-1932 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
ELIAS C. VAGENAS
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quasinormal Modes ◽  
Kerr Black Hole ◽  
Area Spectrum ◽  
The Real ◽  
Hole Area ◽  
Newman Black Hole ◽  
Discrete Area ◽  
Kerr Black Holes

Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form mΩ where Ω is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly spaced. Thus, we infer that the function describing the real part of quasinormal frequencies of Kerr black hole is not the correct one. This conclusion is in agreement with the numerical results for the highly damped quasinormal modes of Kerr black hole recently presented by Berti, Cardoso and Yoshida. On the contrary, extremal Kerr black hole is shown to have a discrete area spectrum which in addition is evenly spaced. The area spacing derived in our analysis for the extremal Kerr black hole area spectrum is not proportional to ln 3. Therefore, it does not give support to Hod's statement that the area spectrum [Formula: see text] should be valid for a generic Kerr–Newman black hole.

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