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We develop a new method for writing simple exact equations characterizing gravity solutions among which black holes and in particular the quasinormal modes. More precisely, we derive the full system of functional and Thermodynamic Bethe…
We apply the complex scaling method to black-hole perturbations in four-dimensional Schwarzschild--de~Sitter (dS) spacetimes. The method converts the outgoing-wave boundary-value problem into a non-Hermitian spectral problem and enables…
We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In…
I discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild black hole, I expand around the zeroth-order approximation to the wave equation…
The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are…
We study the quasinormal modes (QNMs) of dilaton black holes in Einstein-Maxwell-dilaton gravity through a correspondence with the quantum Seiberg-Witten (SW) curve of $\mathcal{N}=2$ SU(2) gauge theory with $N_f=3$ hypermultiplets. By…
We present a comprehensive analysis of the quasinormal modes (QNMs) of a massive scalar field in Schwarzschild spacetime using two complementary numerical techniques: the Hill-determinant method and Leaver continued-fraction method. Our…
In this paper, we provide a comprehensive survey of possible applications of the matrix method for black hole quasinormal modes. The proposed algorithm can generally be applied to various background metrics, and in particular, it…
The nonlinear superposition of the delta-metric and the Kerr metric results in delta-Kerr metric that represents a deformed Kerr black hole with delta = 1 + q, where q > 0 is proportional to the nonrelativistic quadrupole moment of the…
The deviations of non-linear perturbations of black holes from the linear case are important in the context of ringdown signals with large signal-to-noise ratio. To facilitate a comparison between the two we derive several results of linear…
We study the quasi-normal modes of the charged scalar perturbations in the background of the Einstein-Maxwell-aether black hole through three methods (WKB method, continued fraction method, generalized eigenvalue method). Then we propose…
We investigate the quasinormal modes (QNMs) of noncommutative geometry-inspired dirty black holes, focusing on both non-extremal and extremal configurations. These gravitational objects, characterized by smeared energy distributions within…
Newton's method for polynomial root finding is one of mathematics' most well-known algorithms. The method also has its shortcomings: it is undefined at critical points, it could exhibit chaotic behavior and is only guaranteed to converge…
A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Here we explore some of its infinitely many generalizations to two dimensions,…
Recent works have suggested that nonlinear (quadratic) effects in black hole perturbation theory may be important for describing a black hole ringdown. We show that the technique of uniform approximations can be used to accurately compute…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
We study the quasinormal modes of the spherically-symmetric $(2+1)$-dimensional analogue black hole, modeled by the ``draining bathtub'' fluid flow, and the $(3+1)$-dimensional canonical acoustic black hole. In the both cases the emphasis…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs,…
We explore quasinormal modes (QNMs) of the Schwarzschild black hole under a noncommutative (NC) deformation of spacetime, constructed via a Drinfeld twist formalism. In this approach, the usual Regge--Wheeler (axial) and Zerilli (polar)…