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 …

We present a novel method that solves Teukolsky equations with the source to calculate
radiation fluxes at infinity and event horizon for any perturbation fields of type-D black holes …

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 …

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 …

A bstract We study the scattering of a massless scalar field in a generic Kerr background.
Using a particular gauge choice based on the current conservation of the radial equation …

Weak gravitational, electromagnetic, neutrino and scalar fields, considered as perturbations
on Kerr background satisfy Teukolsky Master Equation. The two non-trivial equations …

We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH)
or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects …

We present new developments of the simple model of the central engine of GRB, proposed
recently. The model is based on minimal assumptions: some rotating compact relativistic …

We summarize recent results by the authors in Refs. 1, 2, 3 on the extraction of scattering
amplitudes for scalar fields in Kerr/Kerr-de Sitter backgrounds. Analytical, closed forms are …

The main objective of this thesis is study the spectrum of rotating compact massive objects
using the linearized perturbation theory developed by Teukolsky. To achieve this goal, we …