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The Heun functions have wide application in modern physics and are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functions, however, is complicated and…
This work discusses the Improved Matrix Method and Weighted Residual Method for studying the quasinormal modes (QNMs) of black holes. In the first method, by utilizing Jordan decomposition, the improved matrix method avoids the calculation…
We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from…
Based on the work of Chen, L\"u and Pope, we derive expressions for the $D\geq 6$ dimensional metric for Kerr-(A)dS black holes with two independent rotation parameters and all others set equal to zero: $a_1\neq 0, a_2\neq0, a_3=a_4=...=0$.…
We discuss new recurrence-based methods for calculating the complex frequencies of the quasinormal modes of black holes. These methods are based on the Frobenius series solutions of the differential equation describing the linearized radial…
We present a novel approach to the numerical computation of quasi-normal modes, based on the first-order (in radial derivative) formulation of the equations of motion and using a matrix version of the continued fraction method. This…
Studies of quasinormal modes (QNMs) of black holes have a long and well established history. Predominantly, much research in this area has customarily focused on the equations given by Regge, Wheeler and Zerilli. In this work we study…
We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations. We introduce the standard version of this method…
Quasinormal mode (QNM) spectra of black holes exhibit two open problems [Conf. Proc. C 0405132, 145 (2004); CQG 26, 163001 (2009)]: (i) the discontinuity in highly damped QNMs between Schwarzschild and Kerr solutions as $a \to 0$, and (ii)…
We discuss simple integration methods for the calculation of rotating black hole scattering resonances both in the complex frequency plane (quasinormal modes) and the complex angular momentum plane (Regge poles). Our numerical schemes are…
In this paper, a quantum dot mathematical model based on a two-dimensional Schr\"odinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a…
The ringdown of perturbed black holes has been studied since the 1970s, but until recently, studies have focused on linear perturbations. There is now burgeoning interest in nonlinear perturbative effects during ringdown. Here, using a…
We revisit the computation of quasinormal modes (QNMs) of the Kerr black hole using a numerical approach exploiting a representation of the Teukolsky equation as a $2D$ elliptic partial differential equation. By combining the hyperboloidal…
Using gravitational waves to probe the geometry of the ringing remnant black hole formed in a binary black hole coalescence is a well-established way to test Einstein's theory of general relativity. However, doing so requires knowledge of…
We study black-hole quasinormal modes by applying the complex scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner--Nordstr\"om black holes. The method converts the outgoing-wave boundary condition into a…
We develop a quantum optical framework for probing black hole quasinormal modes (QNMs) using two-level atoms in the spirit of the horizon-brightened acceleration radiation (HBAR) program. Starting from the QNM contribution to the Wightman…
The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence offers an efficient analytical approach to calculate the QNM frequencies, which was only available numerically before. This is based on the fact that both…
We study the quasinormal modes (QNMs) of the Schwarzschild black hole immersed in an electromagnetic (em) universe. The immersed Schwarzschild black hole (ISBH) is originated from the metric of colliding em waves with double polarization…
Although finding numerically the quasinormal modes of a nonrotating black hole is a well-studied question, the physics of the problem is often hidden behind complicated numerical procedures aimed at avoiding the direct solution of the…
In this work, we study the quasinormal modes of Schwarzschild and Schwarzschild (Anti-) de Sitter black holes by a matrix method. The proposed method involves discretizing the master field equation and expressing it in form of a homogeneous…