arXiv subjects

Fawzi Aly

Publications and source records attributed to Fawzi Aly.

6 recordsLinked to original sources

arXiv2026

How it cools? Studying the heat flow out of a semi-infinite slab in welding: An analytical approach

Additive manufacturing and welding processes are highly sensitive to heat dissipation, where improper thermal management leads to residual stresses, distortions, and cracking. Existing heat transfer models, such as Rosenthal's solutions, fail to handle finite 3D geometries, cooling effects, or transient behavior, limiting their accuracy. We overcome these limitations by developing an analytical framework that incorporates cooling boundary conditions mimicking Newton's Law of Cooling. Using two different and proven-equivalent approaches, Laplace transform and Fourier series, we derive closed-form solutions for transient and steady-state temperature profiles under various heat sources, including Gaussian, ellipsoidal, double-ellipsoidal, and time-dependent on/off switch sources. We compare our analytical solutions to numerical implementations, demonstrating strong agreement while providing deeper physical insight. This approach significantly reduces computational cost and experimental requirements, making it a scalable tool for optimizing thermal predictions and mitigating residual stresses in metal-based manufacturing. Additionally, our framework enables the generation of synthetic datasets for machine learning models to predict heat distribution efficiently.

math-ph↗

arXiv2026

Modified Teukolsky formalism: Null testing and numerical benchmarking

Next-generation gravitational-wave detectors will make black-hole ringdown an increasingly sensitive probe of small departures from General Relativity in the strong-field regime. This motivates obtaining high-precision predictions of gravitational effective field theory, as spectral shifts can be quite small. Here we perform a focused stress test of the modified-Teukolsky framework by designing two null diagnostics. First, we consider an action with redundant operators that must produce zero first-order vacuum QNM shifts. Second, we exploit a Ricci-flat identity relating two physical cubic Riemann to test such a relation is satisfied by the ringdown spectra obtained. We compute the shifts using two independent numerical approaches: the eigenvalue-perturbation and generalized continued-fraction (Leaver-type) methods. Both null tests are passed across multiple multipoles and overtones, and the control-operator results agree in magnitude with the benchmark values reported in Ref. [1]. These validations support using the framework for obtaining accurate predictions for robust strong-field tests, with straightforward extensions to rotating backgrounds and coupling with matter fields.

gr-qc↗

arXiv2025

Coupling between gravitational and electromagnetic perturbations on Kerr Spacetime

We extend our previous Schwarzschild metric-based studies of gravitational--electromagnetic (GEM) coupling to rotating black holes by working directly in a curvature-based Newman--Penrose/Teukolsky framework on Kerr spacetime. Within a minimally coupled Einstein--Maxwell system, we derive explicit quadratic electromagnetic source terms for the spin-$-2$ Teukolsky equation, providing a foundation for future numerical studies of GEM interactions in the framework of black-hole spectroscopy. Moreover, we give order-of-magnitude arguments showing that GEM quadratic quasinormal modes (QQNMs) can become relevant in a range of charged and magnetized astrophysical scenarios. Finally, we show through a brief dilaton-theory example that the GEM QQNM spectrum is sensitive to how gravity couples to electromagnetism, thereby providing a model-based way to test minimal coupling and to constrain hidden $U(1)$ sectors with gravitational-wave observations.

gr-qc↗

arXiv2025

More Nonlinearities? II. A Short Guide of First- and Second-Order Electromagnetic Perturbations in the Schwarzschild Background

We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In addition to the induced mixed quadratic modes, we find that linear gravitational modes are also excited, with amplitudes dependent on the electromagnetic potential. A toy model involving a Dirac delta function potential demonstrates mixing of linear gravitational and electromagnetic perturbations with frequencies $ ω^{(1)} $ and $ Ω^{(1)} $, resulting in the second-order QNM mixing in the electromagnetic field at $ Ω^{(2)} =Ω^{(1)} + ω^{(1)} $. This complements prior work in \cite{aly2024nonlinearities} on the second-order gravitational perturbation mixing and highlights potential applications in multi-messenger astrophysics for systems observed by LIGO-Virgo-KAGRA (LVK) and upcoming LISA. We also study first-order perturbations due to a point charge and show it could be reduced to a one-dimensional path integral. Within the toy model, we investigate the first-order electromagnetic perturbation due to a radially free-falling single charge $ q $ and radial dipole moment $ p = q η$, employing semi-analytical and numerical methods. For the dipole case, we show that the QNM perturbation is excited with a nearly constant amplitude. Future work will focus on incorporating mixing in more realistic potentials and exploring numerical approach in the context of rotating spacetimes.

gr-qc↗

arXiv2024

More Nonlinearities? Electromagnetic and Gravitational Mode Mixing in NSBH Mergers

We investigate the possibility of electromagnetic fields leaving imprints on gravitational wave (GW) signals from Neutron Star-Black hole (NSBH) mergers, specifically in the context of extreme mass ratio inspirals (EMRIs). Using black hole perturbation theory (BHPT) in the context of a minimally coupled Einstein-Maxwell system, we demonstrate that electromagnetic quasi normal modes(QNMs) can excite gravitational QNMs with frequencies that are linear or quadratic in the electromagnetic QNMs, at first level of mixing. Moreover, We then study the electromagnetism-gravity coupling by approximating the Regge-Wheeler and Zerilli potentials with Dirac delta functions. In this example, we examine gravitational perturbations induced by the electromagnetic field of an ideal dipole radially free fall towards the blackhole, building on calculations from a companion paper [1]. Our results show that both linear and quadratic electromagnetic QNMs appear in gravitational perturbations. In addition, linear gravitational QNMs are also excited due to the electromagnetic source, with their amplitudes depending on the details of the electromagnetic and gravitational potentials, analogous to gravitational mode mixing analysis. Furthermore, at late stages, gravitational perturbations might exhibit polynomial tails induced by electromagnetic perturbations. This article sets the stage for future numerical investigations aimed at identifying such modes in various scenarios.

gr-qc↗

arXiv2023

In Horizon Penetrating Coordinates: Kerr Black Hole Metric Perturbation Construction and Completion

We investigate the Teukolsky equation in horizon-penetrating coordinates to study the behavior of perturbation waves crossing the outer horizon. For this purpose, we use the null ingoing/outgoing Eddington-Finkelstein coordinates. The first derivative of the radial equation is a Fuchsian differential equation with an additional regular singularity to the ones the radial one has. The radial functions satisfy the physical boundary conditions without imposing any regularity conditions. We also observe that the Hertz-Weyl scalar equations preserve their angular and radial signatures in these coordinates. Using the angular equation, we construct the metric perturbation for a circularly orbiting perturber around a black hole in Kerr spacetime in a horizon-penetrating setting. Furthermore, we completed the missing metric pieces due to the mass M and angular momentum J perturbations. We also provide an explicit formula for the metric perturbation as a function of the radial part, its derivative, and the angular part of the solution to the Teukolsky equation. Finally, we discuss the importance of the extra singularity in the radial derivative for the convergence of the metric expansion.

gr-qc↗