Quasi-normal oscillations of a schwarzschild black hole

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past ten years in string theory, brane-world models and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes (QNMs), allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, AdS/CFT interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

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“…This gap can be approximated by a potential for which we know the analytic solution of the wave equation: It is the Pöschl-Teller potential 33 ,…”

Section: B the Mashhoon Methods: Approximation With The Pöschl-tellermentioning

confidence: 99%

Quasinormal modes of black holes: From astrophysics to string theory

2011

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“…The simplest one consists in approximating the black hole potential by a Pöschl-Teller potential whose analytical solutions are known [3]. Another * mauricio.richartz@ufabc.edu.br approximation technique is the WKB method [4], which is equivalent to finding the poles of the transmission coefficient of a tunnelling problem in Quantum Mechanics.…”

Section: Introductionmentioning

confidence: 99%

Quasinormal modes of extremal black holes

Richartz

2016

Phys. Rev. D

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The continued fraction method (also known as Leaver's method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for neutral massless fields around an extremal Reissner-Nordström black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordström black hole and to neutral massless perturbations around an extremal Kerr black hole. In particular, the existence of damped modes is analysed in detail. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed. Mode stability of extremal black holes is also investigated.

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“…The following non-exhaustive classification was outlined in [24]: (i) Time domain methods, whereby the least-damped frequencies are extracted from long, stable time evolutions [5,25]; (ii) Direct integration in the frequency domain as pioneered in [26]; (iii) Inverse potential methods whereby the 'exact' potential is replaced with a simple potential whose spectrum is known [27]; (iv) WKB methods adapted from standard techniques in quantum mechanics [28,29,30,31]; (v) Phase-integral methods using integration along anti-Stokes lines in the complex-r plane [32,33,11]; (vi) Continued fraction methods, first employed in the 1930s to find electronic spectrum of the H + ion, and adapted to black holes by Leaver [34]. The relative advantages and disadvantages of these methods are discussed in several review articles [1,2,4].…”

Section: Existing Methods For Determining Qnmsmentioning

confidence: 99%

On an expansion method for black hole quasinormal modes and Regge poles

Dolan¹,

Ottewill²

2009

Class. Quantum Grav.

178

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Abstract. We present a new method for determining the frequencies and wavefunctions of black hole quasinormal modes (QNMs) and Regge poles. The key idea is a novel ansatz for the wavefunction, which relates the high-l wavefunctions to null geodesics which start at infinity and end in perpetual orbit on the photon sphere. Our ansatz leads naturally to the expansion of QNMs in inverse powers of L = l + 1/2 (in 4D), and to the expansion of Regge poles in inverse powers of ω. The expansions can be taken to high orders. We begin by applying the method to the Schwarzschild spacetime, and validate our results against existing numerical and WKB methods. Next, we generalise the method to treat static sphericallysymmetric spacetimes of arbitrary spatial dimension. We confirm that, at lowest order, the real and imaginary components of the QNM frequency are related to the orbital frequency and the Lyapunov exponent for geodesics at the unstable orbit. We apply the method to five spacetimes of current interest, and conclude with a discussion of the advantages and limitations of the new approach, and its practical applications.

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Quasi-normal oscillations of a schwarzschild black hole

Cited by 127 publications

References 5 publications

Quasinormal modes of black holes: From astrophysics to string theory

Quasinormal modes of black holes: From astrophysics to string theory

Quasinormal modes of extremal black holes

On an expansion method for black hole quasinormal modes and Regge poles

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