A numerically accurate investigation of black-hole normal modes

1992 ◽  
Vol 439 (1905) ◽  
pp. 47-58 ◽  
Keyword(s):  
Black Hole ◽  
Normal Mode ◽  
Gravitational Collapse ◽  
Normal Modes ◽  
High Accuracy ◽  
Late Time ◽  
Schwarzschild Black Hole ◽  
Amplitude Analysis ◽  
Phase Amplitude ◽  
Very High

The oscillations of a Schwarzschild black hole, describing the late time ringing expected after, for example, a gravitational collapse, are discussed in terms of the characteristic normal-mode frequencies. A condition determining these frequencies is derived within the phase-amplitude method. The numerical results obtained using this condition are of very high accuracy, and the phase-amplitude analysis seems to provide a powerful alternative to the previous investigations of the normal-mode problem.

scholarly journals Black hole S-matrix for a scalar field

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Panos Betzios ◽  
Nava Gaddam ◽  
Olga Papadoulaki
Keyword(s):  
Black Hole ◽  
Normal Modes ◽  
Massless Scalar ◽  
Scattering Process ◽  
Schwarzschild Black Hole ◽  
Asymptotically Flat ◽  
Scalar Particles ◽  
Black Hole Background ◽  
S Matrix ◽  
Do So

Abstract We describe a unitary scattering process, as observed from spatial infinity, of massless scalar particles on an asymptotically flat Schwarzschild black hole background. In order to do so, we split the problem in two different regimes governing the dynamics of the scattering process. The first describes the evolution of the modes in the region away from the horizon and can be analysed in terms of the effective Regge-Wheeler potential. In the near horizon region, where the Regge-Wheeler potential becomes insignificant, the WKB geometric optics approximation of Hawking’s is replaced by the near-horizon gravitational scattering matrix that captures non-perturbative soft graviton exchanges near the horizon. We perform an appropriate matching for the scattering solutions of these two dynamical problems and compute the resulting Bogoliubov relations, that combines both dynamics. This allows us to formulate an S-matrix for the scattering process that is manifestly unitary. We discuss the analogue of the (quasi)-normal modes in this setup and the emergence of gravitational echoes that follow an original burst of radiation as the excited black hole relaxes to equilibrium.

scholarly journals QUASI-NORMAL MODES OF SCHWARZSCHILD–ANTI-DE SITTER BLACK HOLES: ELECTROMAGNETIC AND GRAVITATIONAL PERTURBATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2752-2752
Author(s):  
VITOR CARDOSO ◽  
JOSÉ P. S. LEMOS
Keyword(s):  
Black Hole ◽  
Imaginary Part ◽  
Normal Modes ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Small Black Hole ◽  
Conformal Field ◽  
Gravitational Perturbations ◽  
Ads Spacetime ◽  
Electromagnetic Perturbation

We studied the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically anti-de Sitter (AdS) spacetime, extending previous works1,2 on the subject. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar1 and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole3 in an asymptotically flat spacetime: the imaginary part of the frequency goes as [Formula: see text], where r+ is the horizon radius. We also investigated the small black hole limit showing that the imaginary part of the frequency goes as [Formula: see text]. These results are important to the AdS/CFT4 conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory. For other geometries see5,6.

scholarly journals Geodesic stability and quasi normal modes via Lyapunov exponent for Hayward black hole

2020 ◽  
Vol 35 (30) ◽  
pp. 2050249
Author(s):  
Monimala Mondal ◽  
Parthapratim Pradhan ◽  
Farook Rahaman ◽  
Indrani Karar
Keyword(s):  
Black Hole ◽  
Lyapunov Exponent ◽  
Time Scale ◽  
Proper Time ◽  
Normal Modes ◽  
Schwarzschild Black Hole ◽  
Coordinate Time ◽  
Stability And Instability ◽  
The Stability ◽  
Asymptotic Observers

We derive proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] for a regular Hayward class of black hole. The proper time corresponds to [Formula: see text] and the coordinate time corresponds to [Formula: see text], where [Formula: see text] is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as [Formula: see text] for time-like geodesics. In the limit of [Formula: see text] that means for Schwarzschild black hole this ratio reduces to [Formula: see text]. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

scholarly journals NUMERICAL SIMULATION OF QUASI-NORMAL MODES IN TIME-DEPENDENT BACKGROUND

2004 ◽  
Vol 19 (03) ◽  
pp. 239-252 ◽  
Author(s):  
LI-HUI XUE ◽  
ZAI-XIONG SHEN ◽  
BIN WANG ◽  
RU-KENG SU
Keyword(s):  
Numerical Simulation ◽  
Black Hole ◽  
Wave Propagation ◽  
Normal Modes ◽  
Time Dependent ◽  
Massless Scalar ◽  
Scalar Wave ◽  
Schwarzschild Black Hole ◽  
Black Hole Background ◽  
Scattering Potential

We study the massless scalar wave propagation in the time-dependent Schwarzschild black hole background. We find that the Kruskal coordinate is an appropriate framework to investigate the time-dependent spacetime. A time-dependent scattering potential is derived by considering dynamical black hole with parameters changing with time. It is shown that in the quasinormal ringing both the decay time-scale and oscillation are modified in the time-dependent background.

Black hole spectroscopy from a class of Plebański and Demiański space–times

2014 ◽  
Vol 92 (1) ◽  
pp. 46-50
Author(s):  
De-Jiang Qi
Keyword(s):  
Black Hole ◽  
Normal Modes ◽  
Kerr Black Hole ◽  
Black Hole Thermodynamics ◽  
Area Spectrum ◽  
Spherically Symmetric ◽  
Adiabatic Invariance ◽  
Schwarzschild Black Hole ◽  
Gravity System ◽  
Area Spectra

Recently, via adiabatic invariance, Majhi and Vagenas quantized the horizon area of the general class of a static spherically symmetric space–time. Very recently, applying the period of the gravity system with respect to the Euclidean time, Zeng and Liu derived area spectra of a Schwarzschild black hole and a Kerr black hole. It is noteworthy that the preceding methods are not useful for the quasi-normal modes. In this paper, based on those works, and as a further study, adopting near horizon approximation, applying the laws of black hole thermodynamics, we would like to investigate the black hole spectroscopy from a class of Plebański and Demiański space–times by using two different methods. The result shows that the area spectrum of the black hole is [Formula: see text], which confirms the initial proposal of Bekenstein, and the result is consistent with that already obtained by Maggiore with quasi-normal modes.

Normal-mode frequencies of Reissner–Nordström black holes

1993 ◽  
Vol 442 (1915) ◽  
pp. 427-436 ◽  
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Numerical Integration ◽  
Normal Mode ◽  
Characteristic Frequency ◽  
Continued Fraction ◽  
Higher Order ◽  
Coordinate Plane ◽  
Phase Amplitude

The normal-mode frequencies of a Reissner–Nordström black hole are determined from a phase-amplitude formula, using numerical integration in the complex coordinate plane. The results obtained are numerically very accurate, extending previous higher-order WKB results of Kokkotas and Schutz as well as the continued fraction results of Leaver. The change in the characteristic frequency of each mode as the charge of the black hole increases is also discussed.

DECAY OF MASSIVE DIRAC HAIRS ON BRANE-WORLD BLACK HOLES

2008 ◽  
Vol 17 (11) ◽  
pp. 2065-2078
Author(s):  
JILIANG JING ◽  
QIYUAN PAN ◽  
CHIKUN DING
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Decay Rate ◽  
Time Evolution ◽  
Wave Mode ◽  
Brane World ◽  
Late Time ◽  
Schwarzschild Black Hole ◽  
Dirac Fields

The late-time evolution of massive Dirac fields in the backgrounds of brane-world black holes is investigated. We find that the dumping exponent depends on both the multiple number of the wave mode and the mass of the Dirac fields, but almost does not depend on the parameter ϒ of the brane-world black holes. We also find that the decay rate of the asymptotic late-time tail is t-5/6. Our results show that the decay of massive Dirac hairs on brane-world black holes has the same behavior as that of the Schwarzschild black hole.

scholarly journals Quantum corrections to the accretion onto a Schwarzschild black hole in the background of quintessence

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Kourosh Nozari ◽  
Milad Hajebrahimi ◽  
Sara Saghafi
Keyword(s):  
Black Hole ◽  
Quantum Fluctuations ◽  
Radial Component ◽  
Quantum Corrections ◽  
Back Reaction ◽  
Late Time ◽  
Candidate Model ◽  
Schwarzschild Black Hole ◽  
Singularity Point ◽  
Quintessence Field

AbstractIt is well known that quantum effects may lead to removal of the intrinsic singularity point of back holes. Also, the quintessence scalar field is a candidate model for describing late-time acceleration expansion. Accordingly, Kazakov and Solodukhin considered the existence of back-reaction of the spacetime due to the quantum fluctuations of the background metric to deform a Schwarzschild black hole, which led to a change of the intrinsic singularity of the black hole to a 2-sphere with a radius of the order of the Planck length. Also, Kiselev rewrote the Schwarzschild metric by taking into account the quintessence field in the background. In this study, we consider the quantum-corrected Schwarzschild black hole inspired by Kazakov–Solodukhin’s work, and the Schwarzschild black hole surrounded by quintessence deduced by Kiselev to study the mutual effects of quantum fluctuations and quintessence on the accretion onto the black hole. Consequently, the radial component of the 4-velocity and the proper energy density of the accreting fluid have a finite value on the surface of its central 2-sphere due to the presence of quantum corrections. Also, by comparing the accretion parameters in different kinds of black holes, we infer that the presence of a point-like electric charge in the spacetime is somewhat similar to some quantum fluctuations in the background metric.

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