Exact solutions of the angular Teukolsky equation for particular cases

Classes of Exact Solutions to the Teukolsky Master Equation

The Teukolsky Master Equation describes 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 and the confluent Heun polynomials. Large classes of...

Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.

Classes of Exact Solutions to Regge-Wheeler and Teukolsky Equations

The Regge-Wheeler equation describes axial perturbations of Schwarzschild metric in linear approximation. Teukolsky Master Equation describes perturbations of Kerr metric in the same approximation. We present here unified description of all classes of exact solutions to these equations in terms of the confluent Heun’s functions. Special attention is paid to the polynomial solutions, which yield...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow

Decay of Solutions of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry

We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin s = 1 or s = 2, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in L∞loc.