Related papers: Bernstein spectral method for quasinormal modes an…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
Quasinormal modes and frequencies are the eigenvectors and eigenvalues of a non-Hermitian differential operator. They hold crucial significance in the physics of black holes. The analysis of quasinormal modes of black holes in…
A key obstacle for theory-specific tests of general relativity is the lack of accurate black-hole solutions in beyond-Einstein theories, especially for moderate to high spins. We address this by developing a general framework--based on…
Recent investigations of the pseudospectrum in black hole spacetimes have shown that quasinormal mode frequencies suffer from spectral instabilities. This phenomenon may severely affect gravitational-wave spectroscopy and limit precision…
Analyzing the stability of quasinormal modes (QNM) is essential for understanding black hole dynamics, particularly in the context of gravitational wave emissions and black hole spectroscopy. In this study, we employ the hyperboloidal…
In the spectral Petrov-Galerkin methods, the trial and test functions are required to satisfy particular boundary conditions. By a suitable linear combination of orthogonal polynomials, a basis, that is called the modal basis, is obtained.…
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…
In this paper, we present a detailed study of axial gravitational perturbations of the regular black hole solution in asymptotically safe gravity, as proposed in \cite{Bonanno:2023rzk}. We analyze the quasinormal mode (QNM) spectrum of this…
We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the…
The Newman-Penrose formalism is used to deal with the massless scalar, neutrino, electromagnetic, gravitino and gravitational quasinormal modes (QNMs) in Schwarzschild black holes in a united form. The quasinormal mode frequencies evaluated…
We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Schwarzschild, BTZ, extremal Reissner-Nordstr\"om, near extremal Schwarzschild-de Sitter, and Kerr black holes. Based on the…
We investigate the scalar, gravitational, and electromagnetic quasinormal mode spectra of Schwarzschild anti-de Sitter black holes using the numerical continued fraction method. The spectra have similar, almost linear structures. With a few…
In this study, we investigate the pseudospectrum and spectrum (in)stability of quantum corrected Schwarzschild black hole. Methodologically, we use the hyperboloidal framework to cast the quasinormal mode (QNM) problem into an eigenvalue…
We calculate the quasinormal modes of a nonsingular spherically symmetric black hole effective model with holonomy corrections. The model is based on quantum corrections inspired by loop quantum gravity. It is covariant and results in a…
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…
In this work we present an explicit representation of the orthonormal Bernstein polynomials and demonstrate that they can be generated from a linear combination of non-orthonormal Bernstein polynomials. In addition, we report a set of $n$…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
In this article, we study numerical approximation of eigenvalue problems of the Schr\"{o}dinger operator $\displaystyle -\Delta u + \frac{c^2}{|x|^2}u$. There are three stages in our investigation: We start from a ball of any dimension, in…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…