Related papers: Choosing the phase for the spin-weighted spheroida…
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…
Spin-weighted spheroidal harmonics play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering. We present a novel and compact derivation of the asymptotic…
Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the…
Prolate spin-weighted spheroidal harmonics play a key role in black-hole perturbation theory. In particular, the highly damped quasinormal resonances of rotating Kerr black holes are closely related to the asymptotic eigenvalues of these…
The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-potential in the series of the parameter…
The angular dependence of the gravitational radiation emitted in compact binary mergers and gravitational collapse is usually separated using spin-weighted spherical harmonics ${}_sY_{\ell m}$ of spin weight $s$, that reduce to the ordinary…
While the Teukolsky equation plays a central role in traditional treatments of perturbations of algebraically special spacetimes, its relation to Friedrich's conformal Einstein field equations (CEFEs) remains largely unexplored. Here we…
This paper explains existing results for the application of special functions to phase estimation, which is a fundamental topic in quantum information. We focus on two special functions. One is prolate spheroidal wave function, which…
In this paper, we use the means of super-symmetric quantum mechanics to study of the Spin-weighted Spheroidal Wave in the case of s=3/2. We obtain some interesting results: the first-five terms of the super-potential, the general form of…
We present series study of using the method of super-symmetric quantum mechanics(SUSYQM) solving the spin-weighted spheroidal wave equation. In this paper, we obtain the first four terms of super-potential of the spin-weighted spheroidal…
The measurement of black hole spin is considered one of the key problems in relativistic astrophysics. Existing methods, such as continuum fitting, X-ray reflection spectroscopy and quasi-periodic oscillation analysis, have systematic…
The spheroidal wave functions, which are the solutions to the Helmholtz equation in spheroidal coordinates, are notoriously difficult to compute. Because of this, practically no programming language comes equipped with the means to compute…
The analytical solutions reported in our previous paper are given as series of hypergeometric or Coulomb wave functions. By using them, we can get the Teukolsky functions analytically in a desired accuracy. For the computation, the deep…
In this paper we study the recurrence relations in the spin-weighted spheroidal harmonics (SWSHs) through super-symmetric quantum mechanics. We use the shape invariance property to solve the spin-weighted spheroidal wave equations. The…
It is well known that Teukolsky equation of gravitational perturbations provides a powerful tool for the investigation of the ringdown phase of a binary black hole merger, but it is applicable only for final configurations in the Kerr…
Integral equations for the spin-weighted spheroidal wave functions is given. For the prolate spheroidal wave function with m=0, there exists the integral equation whose kernel is(sin x)/x, and the sinc function kernel (sin x)/x is of great…
We calculate analytically the asymptotic form of quasi-normal modes of perturbations of arbitrary spin of a Schwarzschild black hole including first-order corrections. We use the Teukolsky equation which applies to both bosonic and…
We consider the eikonal phase associated with the gravitational scattering of a highly energetic light particle off a very heavy object in AdS spacetime. A simple expression for this phase follows from the WKB approximation to the…
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is…
In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary…