Quasinormal modes of black holes: from astrophysics to string theory (1102.4014v2)

Abstract: 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.

• The paper synthesizes a decade of developments in QNM research, establishing quasinormal modes as spectral fingerprints of black holes.
• The paper details analytical and numerical methods, including the WKB approximation and Frobenius method, to accurately compute quasinormal spectra.
• The paper applies QNM insights to astrophysics and string theory, offering implications for gravitational wave detection and quantum gravity models.

Quasinormal Modes of Black Holes: From Astrophysics to String Theory

The detailed paper by R. A. Konoplya and A. Zhidenko addresses the multifaceted subject of quasinormal modes (QNMs) and their relevance across various contexts, ranging from astrophysical black holes to applications in string theory and quantum gravity. The paper is organized as a comprehensive review, encapsulating a decade's worth of developments in the paper of QNMs.

Quasinormal Modes: Definition and Relevance

Quasinormal modes refer to the characteristic damped oscillations that occur when black holes undergo perturbations. These oscillations are not merely a theoretical curiosity but are critical in understanding gravitational wave signals emitted by dynamic events such as black hole mergers. The paper establishes the role of QNMs as 'spectral fingerprints' of black holes, offering thorough insights into their gravitational and spacetime properties.

Analytical and Numerical Techniques

Significant attention is devoted to various methods developed for calculating QNM spectra. Among these, the paper details the WKB approximation, Frobenius method, and continued fractions, among others, presenting a toolkit for tackling QNM problems across different scenarios and spacetime configurations. The authors stress the numerical accuracy required in QNM calculations due to their implications for black hole spectroscopy, particularly in light of evolving gravitational wave observatories.

Contextual Applications

1. Astrophysical Black Holes: The QNMs of Schwarzschild, Reissner-Nordström, and Kerr black holes are discussed with implications for real-world gravitational wave observations. A pivotal aspect is the potential observation of these modes through detectors such as LIGO and Virgo, which might unveil the nature of black holes and test general relativity under extreme conditions.
2. Higher Dimensional and AdS/CFT Contexts: The paper navigates through the quasinormal spectra of higher-dimensional black holes pertinent to models with large extra dimensions and string theories like the AdS/CFT correspondence. Here, QNMs provide insights into the thermalization processes in dual CFTs and gauge/gravity duality.
3. Quantum Gravity and Loop Implications: Notably, QNMs have been mooted to hint at the quantum structure of spacetime, potentially influencing loop quantum gravity models. The spacing in the spectrum of QNMs could imply information about black hole area quantization, offering tantalizing connections with the Barbero-Immirzi parameter.

Stability and Tails

A recurring theme in the analysis of QNMs is stability. Utilizing QNMs, the authors discuss criteria for stability against perturbations, crucial for understanding whether certain solutions, like higher-dimensional black strings or particular AdS spacetimes, can exist in nature. The late-time behavior or 'tails' of perturbation fields, especially the distinction between massless and massive field evolutions, is particularly underscored for its implications in both astrophysical and theoretical regimes.

Implications and Future Directions

The research on QNMs cuts across various advanced topics in theoretical physics and gravitational wave astronomy. The paper encourages further exploration into the intersections of QNMs with holography, stability analysis, and observational astrophysics. This multidimensional approach reflects an ongoing synergy in theoretical and experimental domains, seamlessly connecting black hole physics with quantum gravity hypotheses and the frontiers of astrophysical observations.

In conclusion, the paper stands as a robust synthesis of classical and contemporary insights into quasinormal modes, advocating for their broader applicability and future exploration in both established and novel realms of high-energy physics and general relativity.