Superstring theoryをめぐって(放談室)

Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.

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Quasinormal modes of black holes and black branes

Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past 10 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, 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, anti--de Sitter/conformal field theory interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

Quasinormal modes of black holes: From astrophysics to string theory

The present paper reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's functions are introduced and studied. A new alternative derivation of confluent Heun's polynomials is presented.

https://iopscience.iop.org/article/10.1088/1751-8113/43/3/035203/pdf

Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order

The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's functions are introduced and studied. A new alternative derivation of confluent Heun's polynomials is presented.

The well-known Regge–Wheeler equation describes the axial perturbations of the Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved exactly, due to recent mathematical developments. We present the basic properties of its general solution. A novel analytical approach and numerical techniques to study the boundary problems which correspond to quasi-normal modes of black holes and other simple models of compact objects are developed.

Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects

The Teukolsky master equation is the basic tool for the study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky radial equation and the Teukolsky angular equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confluent Heun functions. Large classes of new exact solutions are found and classified with respect to their characteristic properties. Special attention is paid to the polynomial solutions which are singular ones and introduce collimated one-way running waves. It is shown that a proper linear combination of such solutions can present bounded one-way running waves. This type of waves may be suitable as models of the observed astrophysical jets.

https://iopscience.iop.org/article/10.1088/0264-9381/27/13/135001/pdf

Classes of exact solutions to the Teukolsky master equation

The Teukolsky Master Equation is the basic tool for study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky Radial Equation and the Teukolsky Angular Equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confluent Heun functions. Large classes of new exact solutions are found and classified with respect to their characteristic properties. Special attention is paid to the polynomial solutions which are singular ones and introduce collimated one-way-running waves. It is shown that a proper linear combination of such solutions can present bounded one-way-running waves. This type of waves may be suitable as models of the observed astrophysical jets.

Plamen P. Fiziev

Papers

Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order

Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order

Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects

Classes of exact solutions to the Teukolsky master equation

Classes of Exact Solutions to the Teukolsky Master Equation