Plamen P. Fiziev

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

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

Classes of exact solutions to the Teukolsky master equation

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.

Teukolsky-Starobinsky identities: A novel derivation and generalizations

We present a novel derivation of the Teukolsky-Starobinsky identities, based on properties of the confluent Heun functions. These functions define analytically all exact solutions to the Teukolsky master equation, as well as to the Regge-Wheeler and Zerilli ones. The class of solutions, subject to Teukolsky-Starobinsky type of identities is studied. Our generalization of the Teukolsky-Starobinsky identities is valid for the already studied linear perturbations to the Kerr and Schwarzschild metrics, as well as for large new classes of such perturbations which are explicitly described in the present article. Symmetry of parameters of confluent Heuns functions is shown to stay behind the behavior of the known solutions under the change of the sign of their spin weights. A new efficient recurrent method for calculation of Starobinskys constant is described.

Exact solutions of Regge–Wheeler equation and quasi-normal modes of compact objects

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.

Application of the confluent Heun functions for finding the quasinormal modes of nonrotating black holes

Although finding numerically the quasinormal modes of a nonrotating black hole is a well-studied question, the physics of the problem is often hidden behind complicated numerical procedures aimed at avoiding the direct solution of the spectral system in this case. In this article, we use the exact analytical solutions of the Regge-Wheeler equation and the Teukolsky radial equation, written in terms of confluent Heun functions. In both cases, we obtain the quasinormal modes numerically from spectral condition written in terms of the Heun functions. The frequencies are compared with ones already published by Andersson and other authors. A new method of studying the branch cuts in the solutions is presented -- the epsilon-method. In particular, we prove that the mode

ELECTRICALLY CHARGED EINSTEIN–BORN–INFELD BLACK HOLES WITH MASSIVE DILATON

n=8

The spectrum of electromagnetic jets from Kerr black holes and naked singularities in the Teukolsky perturbation theory

is not algebraically special and find its value with more than 6 firm figures of precision for the first time. The stability of that mode is explored using the

Exact solutions of Regge-Wheeler equation

\epsilon

Solving systems of transcendental equations involving the Heun functions

method, and the results show that this new method provides a natural way of studying the behavior of the modes around the branch cut points.

Mathematical Modeling of Boson-Fermion Stars in the Generalized Scalar-Tensor Theories of Gravity

We numerically construct static and spherically symmetric electrically charged black hole solutions in Einstein–Born–Infeld gravity with massive dilaton. The numerical solutions show that the dilaton potential allows many more black hole causal structures than the massless dilaton. We find that depending on the black hole mass and charge and the dilaton mass, the black holes can have either one, two, or three horizons. The extremal solutions are also found. As an interesting peculiarity we note that there are extremal black holes with an inner horizon and with triply degenerated horizon.