Related papers: High-order asymptotics for the Spin-Weighted Spher…
The spheroidal harmonics $S_{lm}(\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena,…
We calculate analytically asymptotic values of quasi-normal frequencies of four-dimensional Kerr black holes by solving the Teukolsky wave equation. We obtain an expression for arbitrary spin of the wave in agreement with Hod's proposal…
It is known that the radial equation of the massless fields with spin around Kerr black holes cannot be solved by special functions. Recently, the analytic solution was obtained by use of the expansion in terms of the special functions and…
We investigate the relativistic scattering of spinning black holes using modern amplitude methods within a heavy-mass effective field theory formalism at third post-Minkowskian order. Using a systematic self-force expansion up to first…
The problem of finding the large order asymptotics for the eigenfunction perturbation theory in quantum mechanics is studied. The relation between the wave function argument x and the number of perturbation theory order k that allows us to…
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…
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…
We consider expansions of eigenvalues and eigenvectors of models of quantum field theory. For a class of models known as generalized spin boson model we prove the existence of asymptotic expansions of the ground state and the ground state…
We investigate the pseudospectrum of the Kerr black hole, which indicates the instability of the spectrum of quasinormal modes (QNMs) of the Kerr black hole. Methodologically, we use the hyperboloidal framework to cast the QNM problem into…
The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated…
In this paper, we provide a rigorous derivation of asymptotic formula for the largest eigenvalues using the convergence estimation of the eigenvalues of a sequence of self-adjoint compact operators of perturbations resulting from the…
We present stationary and axially-symmetric black hole solutions to the Einstein field equations sourced by an anisotropic fluid, describing rotating black holes embedded in astrophysical environments. We compute their physical properties,…
Solutions to the Angular Teukolsky Equation have been used to solve various applied problems in physics and are extremely important to black-hole physics, particularly in computing quasinormal modes and in the extreme-mass-ratio inspiral…
We have proposed in previous papers that the high-frequency pair QPOs observed in black-hole binaries with frequency ratio 3:2 are inertial-acoustic oscillations (nearly horizontal oscillations with no node in the vertical direction) or…
This is a short review of the quasinormal mode spectrum of Schwarzschild, Reissner-Nordstrom and Kerr black holes. The summary includes previously unpublished calculations of i) the eigenvalues of spin-weighted spheroidal harmonics, and ii)…
The spin-weighted spheroidal functions are the eigenfunctions of the angular Teukolsky equation. They are a generalization of the widely used spin-weighted spherical functions, and are extremely important in the area of black-hole…
The present work addresses an axisymmetrically accreting black hole system from three perspectives: the astrophysical, the dynamical systems, and the emergent gravity standpoint. Steady-state equations governing low angular momentum axially…
Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the Cosmic Microwave Background radiation. These objects can be…
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve…
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…