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In recent years there has been an increased interest in neural networks, particularly with regard to their ability to approximate partial differential equations. In this regard, research has begun on so-called physics-informed neural…

One simplified black hole model constructed from a semiclassical analysis of loop quantum gravity (LQG) is called self-dual black hole. This black hole solution depends on a free dimensionless parameter P known as the polymeric parameter…

We explore quantum corrections of electrically charged black holes subject to vacuum polarization effects of fermion fields in QED. Solving this problem exactly is challenging so we restrict to perturbative corrections that one can obtain…

Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of an…

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…

We present a package for Mathematica that facilitates the numerical computation of the quasinormal mode (QNM) spectrum of a black hole/black brane. Requiring as input only the QNM equation(s), the application of a single Mathematica…

To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…

We find new non-supersymmetric solutions of five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are regular, horizonless and have the same asymptotic charges as non-extremal charged black holes. An…

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 study the Klein-Gordon and the Dirac equations in the background of the Garfinkle-Horowitz-Strominger black hole, in the Einstein frame. Using a $SO(3,1) \times U(1)-$gauge covariant approach, as an alternative to the Newman-Penrose…

While independent observations have been made regarding the behaviour of effective quasinormal mode (QNM) potentials within the large angular momentum limit, we demonstrate analytically here that a uniform expression emerges for…

Two numerical methods are used to calculate quasinormal modes (QNMs) of near-extremal black holes/strings in the generalized spherically/cylindrically symmetric background, the Asymptotic Iteration Method (AIM) and the Spectral Method. The…

We present a new method for determining the frequencies and wavefunctions of black hole quasinormal modes (QNMs) and Regge poles. The key idea is a novel ansatz for the wavefunction, which relates the high-$l$ wavefunctions to null…

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…

Firstly, we construct kernels of integral relations among solutions of the confluent Heun equation (CHE) and its limit, the reduced CHE (RCHE). In both cases we generate additional kernels by systematically applying substitutions of…

Tensor and scalar unparticle couplings to matter have been shown to enhance gravitational interactions and provide corrections to the Schwarzschild metric and associated black hole structure. We derive an exact solution to the Einstein…

In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…

Recently we showed how non-homogeneous second-order difference equations appearing within ABJM quantum spectral curve description could be solved using Mellin space technique. In particular we provided explicit results for anomalous…

Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and…

The frequency spectra of the gravito-electromagnetic perturbations of the Kerr-Newman (KN) black hole with the slowest decay rate have been computed recently. It has been found that KN has two families $-$ the photon sphere and the…