arXiv subjects

Lamis Al Sheikh

Publications and source records attributed to Lamis Al Sheikh.

5 recordsLinked to original sources

arXiv2026

A geometric approach to QNMs in optics: application to pseudospectrum and structural stability

We develop a geometric--spectral framework for the computation and stability analysis of quasi-normal modes (QNMs) in open optical cavities of compact support. The hyperboloidal approach, transferred from gravitational physics to electromagnetism [1], incorporates outgoing boundary conditions directly into the formulation of the optical resonance problem. Dispersive and absorbing media are described by a Lorentz-model permittivity through an auxiliary-field formulation, and the resulting non-Hermitian spectral problem is solved using Chebyshev spectral discretization.Pseudospectrum analysis is then extended to the optical setting following [2] and used to study the stability of optical resonances under perturbations. The pseudospectrum provides information on the sensitivity of the resonances that is not contained in the QNM spectrum alone. Particular attention is given to the role of the norm used to define the pseudospectrum, by comparing the stability properties obtained with different choices of scalar product. The results show that the assessment of spectral stability is closely related to the functional setting in which perturbations are measured. Combining the hyperboloidal formulation with pseudospectrum analysis therefore makes it possible to compute optical QNMs while also studying their spectral stability. The approach extends techniques developed for resonance problems in gravitational physics to dispersive electromagnetism and provides a basis for studying stability and sensitivity in open optical systems.

physics.optics↗

arXiv2025

Asymptotics and Universality in Black Holes: from the quasinormal Weyl's law to the binary merger waveform

Current state-of-the-art approaches to black hole (BH) dynamics, encompassing several effective approximation schemes, offer a remarkable control of the quantitative aspects of strong gravity. They also provide key insights into some qualitative aspects of the problem. In spite of this, there remain blind spots that hinder the understanding of the mechanisms underlying some observed phenomena, in particular concerning simplicity and universality in BH spacetimes. Adopting an 'asymptotic reasoning' approach, by filtering non-essential degrees of freedom, can potentially unveil universality patterns by identifying key underlying structural stability mechanisms. We first illustrate such an asymptotic approach by focusing on a BH quasinormal (QNM) Weyl's law, that accounts for the universal asymptotics of the QNM "counting function". This permits to identify light-trapping and the (local) redshift effect as the underlying mechanisms, also offering a bridge to the universal patterns found in BH QNM spectral instability. As a by-product, Weyl's law universality formally opens an observational access to spacetime (effective) dimensionality. More heuristically, we sketch a program recently put forward to apply such 'asymptotic reasoning' to address the observed simplicity and universality patterns in binary BH merger dynamics. This program is built as a hierarchy of asymptotic models, potentially making contact with integrability theory in gravity, namely through the background sector in a "wave-mean flow" approach to BH binary dynamics.

gr-qc↗

arXiv2022

A Weyl's law for black holes

We discuss a Weyl's law for the quasi-normal modes of black holes that recovers the structural features of the standard Weyl's law for the eigenvalues of Laplacian-like operators in compact regions. Specifically, we propose that the asymptotics of the counting function $N(\omega)$ of quasi-normal modes of $(d+1)$-dimensional black holes follows a power-law $N(\omega)\sim \mathrm{Vol}_d^{\mathrm{eff}}\omega^d$, with $\mathrm{Vol}_d^{\mathrm{eff}}$ an effective $d$-volume determined by the light-trapping properties of the black hole geometry. Concretely, the factorisation $\mathrm{Vol}_d^{\mathrm{eff}} \sim \left(8\pi/\kappa\right) \cdot \mathrm{Vol}^{\mathrm{trapped}}_{d-1}$ makes apparent the two underlying structural ingredients, namely the (local) redshift effect controlled by the surface gravity $\kappa$ and the volume $\mathrm{Vol}^{\mathrm{trapped}}_{d-1}$ of the (phase space) trapped set. In particular, this proposal extends the Weyl's law proved by Dyatlov & Zworski for the counting of slowest decaying quasi-normal modes, to include overtones. As an application, these Weyl's laws could provide a probe into the effective spacetime dimensionality, upon the counting of sufficiently many quasi-normal modes in the ringdown signal of binary black hole mergers.

gr-qc↗

arXiv2021

Gravitational wave signatures of black hole quasi-normal mode instability

Black hole (BH) spectroscopy has emerged as a powerful approach to extract spacetime information from gravitational wave (GW) observed signals. Yet, quasinormal mode (QNM) spectral instability under high wave-number perturbations has been recently shown to be a common classical general relativistic phenomenon [1]. This requires to assess its impact on the BH QNM spectrum, in particular on BH QNM overtone frequencies. We conclude: i) perturbed BH QNM overtones are indeed potentially observable in the GW waveform, providing information on small-scale environment BH physics, and ii) their detection poses a challenging data analysis problem of singular interest for LISA astrophysics. We adopt a two-fold approach, combining theoretical results from scattering theory with a fine-tuned data analysis on a highly-accurate numerical GW ringdown signal. The former introduces a set of effective parameters (partially lying on a BH Weyl law) to characterise QNM instability physics. The latter provides a proof-of-principle demonstrating that the QNM spectral instability is indeed accessible in the time-domain GW waveform, though certainly requiring large signal-to-noise ratios. Particular attention is devoted to discuss the patterns of isospectrality loss under QNM instability, since the disentanglement between axial and polar GW parities may already occur within the near-future detection range.

gr-qc↗

arXiv2021

Pseudospectrum and black hole quasi-normal mode (in)stability

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert's pioneer work and Nollert and Price's analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.

gr-qc↗