On the equations governing the gravitational perturbations of the Kerr black hole

1976 ◽  
Vol 350 (1661) ◽  
pp. 165-174 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Kerr Black Hole ◽  
Radial Equation ◽  
One Dimensional ◽  
Gravitational Perturbations ◽  
Dimensional Wave

Teukolsky’s radial equation governing the general, non-axisymmetric, gravitational perturbations of the Kerr black hole is reduced to the form of a one-dimensional wave equation by making use of the transformation which enables the treatment of the non-axisymmetric modes in exactly the same way as the axisymmetric modes.

On the equations governing the axisymmetric perturbations of the Kerr black hole

1975 ◽  
Vol 345 (1641) ◽  
pp. 145-167 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Conservation Laws ◽  
Gravitational Waves ◽  
Kerr Black Hole ◽  
One Dimensional ◽  
Potential Barriers ◽  
Transmission Coefficients ◽  
Dimensional Wave ◽  
Axisymmetric Perturbations

It is shown how Teukolsky’s equation, governing the perturbations of the Kerr black hole, can be reduced, in the axisymmetric case, to a one-dimensional wave equation with four possible potentials. The potentials are implicitly, dependent on the frequency; and besides, depending on circumstances, they can be complex. In all cases (i.e. whether or not the potentials are real or complex), the problem of the reflexion and the transmission of gravitational waves by the potential barriers can be formulated, consistently, with the known conservation laws. It is, further, shown that all four potentials lead to the same reflexion and transmission coefficients.

On the reflexion and transmission of neutrino waves by a Kerr black hole

1977 ◽  
Vol 352 (1670) ◽  
pp. 325-338 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Gravitational Waves ◽  
Kerr Black Hole ◽  
One Dimensional ◽  
Potential Barriers ◽  
Two Component ◽  
Reflexion Coefficient ◽  
Dimensional Wave

The equations governing the two-component neutrino are reduced to the form of a one-dimensional wave equation. And it is shown how the absence of super-radiance (i. e. a reflexion coefficient in excess of one) for incident neutrino waves and its manifestation for incident electromagnetic and gravitational waves (of suitable frequencies) emerge very naturally from the character of the respective potential barriers that surround the Kerr black hole.

The quasi-normal modes of the Schwarzschild black hole

1975 ◽  
Vol 344 (1639) ◽  
pp. 441-452 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Gravitational Waves ◽  
Short Range ◽  
Numerical Solutions ◽  
Normal Modes ◽  
Schwarzschild Black Hole ◽  
One Dimensional ◽  
Potential Barriers ◽  
Dimensional Wave

The quasi-normal modes of a black hole represent solutions of the relevant perturbation equations which satisfy the boundary conditions appropriate for purely outgoing (gravitational) waves at infinity and purely ingoing waves at the horizon. For the Schwarzschild black hole the problem reduces to one of finding such solutions for a one-dimensional wave equation (Zerilli’s equation) for a potential which is positive everywhere and is of short-range. The notion of quasi-normal modes of such one-dimensional potential barriers is examined with two illustrative examples; and numerical solutions for Zerilli’s potential are obtained by integrating the associated Riccati equation.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

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