Search Results for « Quasinormal modes »

We investigate the shear quasinormal modes (QNMs) in the context of electron stars, focusing on the Lifshitz geometry and exploring the behavior in the small star limit. The study begins by analyzing the shear sector modes in the infrared (IR) Lifshitz limit, where the geometry approaches that of a pure Lifshitz space. We derive and solve the differential equations governing the shear modes, revealing the asymptotic behavior in terms of the Lifshitz exponent. In the special case of integer values of the exponent, we obtain analytic corrections to the solutions to extract hydrodynamical QNMs. We then explore the cases with a Lifshitz exponent equal to or greater than three, providing analytical corrections to the Lifshitz IR solutions. A special case with an exponent of two is also considered, leading to modified solutions. The study extends to finding hydrodynamical QNMs, emphasizing the role of the Lifshitz geometry. Further investigations involve the flux with real and complex frequencies, considering the off-shell Lagrangian and deriving conserved flux expressions. Our analysis focuses on the exterior of the star, modeled by the Reissner-Nordström-AdS geometry. The small star limit is examined, revealing interesting features in the behavior of fermionic excitations. In summary, we provide a detailed exploration of shear quasinormal modes in electron stars, shedding light on their behavior in Lifshitz geometry, small star limits, and the interplay between real and complex frequencies. Our findings contribute to our understanding of the dynamics of electron stars and their gravitational properties.

The quasinormal mode (QNM) is generally a mathematical tool in analysing open systems. As the concept of Parity-Time (PT) symmetry was transplanted from quantum mechanics to classical wave systems, massive intriguing phenomena have been found, especially in the vicinity of the so-called exceptional points (EPs). In this paper, with the help of transformation optics (TO), we focus on finding EPs of three-layer PT symmetric models, especially the Metal-Insulator-amplifying Metal (MIaM) ones. Theoretical and numerical methods both indicate that the EPs only exist in the complex frequency regime. Searching within the real frequency spectrum would never find EPs across which complex conjugate wavenumbers occur. Equivalently, only QNMs exist in the symmetry broken phase.

The Bardeen black hole stands as the first model of a regular black hole. Driven by the interpretations of Bardeen spacetime as a quantum-corrected Schwarzschild-like solution, we study quasinormal modes of a massive scalar field within this context. We have found that the damping rate of the massive scalar field decreases as the mass grows, leading to appearance of the arbitrarily long lived modes. or quasiresonances. The massive term in the Bardeen case is distinctive also in two other respects. First, the overtones deviate from their massless limit at a much smaller rate than the fundamental mode, when the mass is turned on. This behavior overlaps with the outburst of overtones due to the quantum deformation near the event horizon. Finally, integration in the time-domain shows that the oscillatory tails decay as $\sim t^{-(\frac{8}{6}+\ell)}$ at intermediate times and as $\sim t^{-1}$ at asymptotically late times, which is different from the Reissner-Nordstr\"om and Schwarzschild limits.

Recently massless test scalar field perturbations of the holonomy corrected black holes [Z. Moreira et. al. Phys. Rev. D 107 (2023) 10, 104016] were studied in order to estimate quantum corrections to the quasinormal spectrum of a black hole. Here we study both the fundamental mode and overtones of scalar, electromagnetic and Dirac fields with the help of the Leaver method and higher order WKB formula with Pad\'e approximants. We observe that the overtones depend on the geometry near the event horizon, while the fundamental mode is localized near the peak of the potential barrier, what agrees with previous studies. We showed that unlike a massless field, the massive one possesses arbitrarily long lived modes. We also obtain the analytical eikonal formula for quasinormal modes and its extension beyond eikonal approximation as a series in powers of $1/\ell$, where $\ell$ is the multipole number.

Micro- and nanoresonators, which enable light trapping in small volumes for extended durations, play a crucial role in modern photonics. The optical response of these resonators is determined by their fundamental resonances, known as quasinormal modes (QNMs). Over the past decade, the electromagnetic theory of QNMs has undergone significant development and has now reached a level of maturity that allows its reliable application to numerous contemporary electromagnetic problems. In this review, we explore recent applications of QNM theory for designing and understanding micro and nanoresonators. We highlight why QNMs provide deep physical insights and enhance computational efficiency in scenarios involving mode hybridization and perturbation.

Oscillations of black hole spacetimes exhibit divergent behavior near the bifurcation sphere and spatial infinity. In contrast, these oscillations remain regular when evaluated near the event horizon and null infinity. The hyperboloidal approach provides a natural framework to bridge these regions smoothly, resulting in a geometric regularization of time-harmonic oscillations, known as quasinormal modes (QNMs). This review traces the development of the hyperboloidal approach to QNMs in asymptotically flat spacetimes, emphasizing both the physical motivation and recent advancements in the field. By providing a geometric perspective, the hyperboloidal approach offers an elegant framework for understanding black hole oscillations, with implications for improving numerical simulations, stability analysis, and the interpretation of gravitational wave signals.