BLACK HOLE AREA SPECTRUM AND ENTROPY SPECTRUM VIA QUASINORMAL MODES IN A QUANTUM CORRECTED SPACETIME

2011 ◽  
Vol 26 (39) ◽  
pp. 2963-2971 ◽  
Author(s):  
CHENG-ZHOU LIU
Keyword(s):  
Black Hole ◽  
Imaginary Part ◽  
Quasinormal Modes ◽  
Area Spectrum ◽  
Entropy Spectrum ◽  
Schwarzschild Black Hole ◽  
The Real ◽  
Hole Area ◽  
Test Particles ◽  
Proper Frequency

The area spectrum and entropy spectrum of the modified Schwarzschild black hole in gravity's rainbow are investigated via the quasinormal modes of the black hole. Using the modified Hod's method and Kunstatter's method that employ the proper frequency from the imaginary part other than the real part of the quasinormal modes, the area and entropy spacing of the black hole are calculated. The results obtained from these two methods agree with each other and the equally spaced area and entropy spectrum are derived. The obtained area and entropy spectrum are independent of the energies of test particles and are the same as from the usual Schwarzschild black hole.

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.

QUASINORMAL MODES OF THE SCHWARZSCHILD BLACK HOLE WITH ARBITRARY SPIN FIELDS: NUMERICAL ANALYSIS

2006 ◽  
Vol 21 (35) ◽  
pp. 2671-2683 ◽  
Author(s):  
QIYUAN PAN ◽  
JILIANG JING
Keyword(s):  
Black Hole ◽  
Quantum Number ◽  
Imaginary Part ◽  
Quasinormal Modes ◽  
Arbitrary Spin ◽  
Schwarzschild Black Hole ◽  
Surprising Effect ◽  
Spin Number ◽  
Spin Fields ◽  
Angular Quantum Number

The quasinormal modes (QNMs) associated with the decay of massless arbitrary spin fields around a Schwarzschild black hole are investigated by using the continued fraction method in a united form and their universal properties are found. It is shown that these QNMs become evenly spaced for large angular quantum number l (for the boson perturbations) and j (for the fermion perturbations) and the spacing is given by [Formula: see text] which is independent of the spin number s and overtone number n, and in the complex plane they have an interesting trend which depends on n before they become the same value with the increasing l (or j). The distribution of the QNMs with arbitrary spin fields for large values l (or j) and small n can be expressed as [Formula: see text]. It is also shown that the angular quantum number has the surprising effect of increasing real part of the QNMs, but it almost does not affect the imaginary part, especially for the lowest lying mode. In addition, the spacing for imaginary part of the QNMs at high overtones is equidistant and equals to -i/4M, which is independent of l (or j) and s.

scholarly journals QUASINORMAL MODES AND LATE-TIME TAILS IN THE BACKGROUND OF SCHWARZSCHILD BLACK HOLE PIERCED BY A COSMIC STRING: SCALAR, ELECTROMAGNETIC AND GRAVITATIONAL PERTURBATIONS

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2505-2524 ◽  
Author(s):  
SONGBAI CHEN ◽  
BIN WANG ◽  
RUKENG SU
Keyword(s):  
Black Hole ◽  
Electromagnetic Fields ◽  
Cosmic String ◽  
Quasinormal Modes ◽  
Late Time ◽  
Gravitational Perturbation ◽  
Schwarzschild Black Hole ◽  
Gravitational Perturbations ◽  
Test Particles

We have studied the quasinormal modes and the late-time tail behaviors of scalar, electromagnetic and gravitational perturbations in the Schwarzschild black hole pierced by a cosmic string. Although the metric is locally identical to that of the Schwarzschild black hole so that the presence of the string will not imprint in the motion of test particles, we found that quasinormal modes and the late-time tails can reflect physical signatures of the cosmic string. Compared with the scalar and electromagnetic fields, the gravitational perturbation decays slower, which would be more interesting to disclose the string effect in this background.

scholarly journals THERMODYNAMICS AND SPECTROSCOPY OF SCHWARZSCHILD BLACK HOLE SURROUNDED BY QUINTESSENCE

2013 ◽  
Vol 28 (04) ◽  
pp. 1350003 ◽  
Author(s):  
R. THARANATH ◽  
V. C. KURIAKOSE
Keyword(s):  
Black Hole ◽  
State Parameter ◽  
Area Spectrum ◽  
Thermodynamic Quantities ◽  
Entropy Spectrum ◽  
Schwarzschild Black Hole ◽  
Quantization Rule ◽  
Euclidean Time ◽  
Special Cases ◽  
Spectroscopic Behavior

The thermodynamic and spectroscopic behavior of Schwarzschild black hole surrounded by quintessence are studied. We have derived the thermodynamic quantities and studied their behavior for different values of quintessence parameter. We put the background spacetime into the Kruskal-like coordinate to find the period with respect to Euclidean time. Also assuming that the adiabatic invariant obeys Bohr–Sommerfeld quantization rule, detailed study of area spectrum and entropy spectrum have been done for special cases of the quintessence state parameter. We find that the spectra are equally spaced.

scholarly journals ASYMPTOTIC QUASINORMAL MODES OF A NONCOMMUTATIVE GEOMETRY INSPIRED SCHWARZSCHILD BLACK HOLE

2007 ◽  
Vol 22 (11) ◽  
pp. 2047-2056 ◽  
Author(s):  
PULAK RANJAN GIRI
Keyword(s):  
Black Hole ◽  
Noncommutative Geometry ◽  
Quasinormal Modes ◽  
Space Time ◽  
Hawking Temperature ◽  
Scalar Perturbation ◽  
Schwarzschild Black Hole ◽  
The Real ◽  
Quasinormal Frequency

We study the asymptotic quasinormal modes for the scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole in 3+1 dimensions. We have considered M ≥ M0, which effectively correspond to a single horizon Schwarzschild black hole with correction due to noncommutativity. We have shown that for this situation the real part of the asymptotic quasinormal frequency is proportional to ln (3). The effect of noncommutativity of space–time on quasinormal frequency arises through the constant of proportionality, which is Hawking temperature TH(θ). We also consider the two-horizons case and show that in this case also the real part of the asymptotic quasinormal frequency is proportional to ln (3).

scholarly journals Black hole spectroscopy via an action invariance in noncommutative spacetimes

2017 ◽  
Vol 26 (1) ◽  
Author(s):  
ChengZhou Liu ◽  
HaiWen Liu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Small Mass ◽  
Area Spectrum ◽  
Back Reaction ◽  
Entropy Spectrum ◽  
Schwarzschild Black Hole ◽  
The One ◽  
Original Derivation ◽  
Noncommutative Parameter

AbstractSpectroscopy for a modified Schwarzschild black hole in noncommutative spacetimes is investigated. By utilizing an action invariance of black holes, the equally spaced entropy spectrum characteristic of Bekenstein’s original derivation is recovered. The derived spectrum is independent of the noncommutative parameter θ, and holds for all the existed noncommutative black holes independent of mass. On the other hand, the obtained area spectrum is not always equidistant due to the noncommutativity effects of the modified spacetimes. For large black holes, the equally spaced area spectrum spectrum can be obtained at the leading order in θ. But, for small black holes, the derived area spectrum is not equidistant, and it depends the noncommutative parameter. In addition, the one loop back reaction effect on the spectroscopy of the noncommutative Schwarzschild black hole is discussed. In this calculation, due to the back reaction effect, the equidistant area spectrum can not be obtained for all the noncommutative black holes with both large and small mass. Conversely, the back reaction effect has no influence on the entropy spectrum. The obtained entropy spectrum is equidistant and consistent with the original Bekenstein’s spectrum for all the existed noncommutative Schwarzschild 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.

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