Perturbation Modes Research Articles

Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part I: Formulation and Odd-Mode Perturbations

This article is Part I of our series of full papers on a gauge-invariant “linear” perturbation theory on the Schwarzschild background spacetime which was briefly reported in our short papers by the present author in 2021. We first review our general framework of the gauge-invariant perturbation theory, which can be easily extended to the “higher-order” perturbation theory. When we apply this general framework to perturbations on the Schwarzschild background spacetime, gauge-invariant treatments of l=0,1 mode perturbations are required. On the other hand, in the current consensus on the perturbations of the Schwarzschild spacetime, gauge-invariant treatments for l=0,1 modes are difficult if we keep the reconstruction of the original metric perturbations in our mind. Due to this situation, we propose a strategy of a gauge-invariant treatment of l=0,1 mode perturbations through the decomposition of the metric perturbations by singular harmonic functions at once and the regularization of these singularities through the imposition of the boundary conditions to the Einstein equations. Following this proposal, we derive the linearized Einstein equations for any modes of l≥0 in a gauge-invariant manner. We discuss the solutions to the odd-mode perturbation equations in the linearized Einstein equations and show that these perturbations include the Kerr parameter perturbation in these odd-mode perturbations, which is physically reasonable. In the Part II and Part III papers of this series of papers, we will show that the even-mode solutions to the linearized Einstein equations obtained through our proposal are also physically reasonable. Then, we conclude that our proposal of a gauge-invariant treatment for l=0,1-mode perturbations is also physically reasonable.

Linear stability of a time-dependent, spherically symmetric background in beyond Horndeski theory and the speed of gravity waves

We address a dynamical, spherically symmetric background in beyond Horndeski theory and formulate a set of linear stability conditions for high energy perturbation modes in the parity odd sector above an arbitrary solution. In this general setting we derive speeds of propagation in both radial and angular directions for the only dynamical degree of freedom in the parity odd sector. We also briefly comment on the propagation speeds of the parity even modes over a dynamical, spherically symmetric background. In particular, we demonstrate that the class of beyond Horndeski theories, which satisfy the equality of gravity waves’ speed to the speed of light over a cosmological background, feature gravity waves propagating at luminal speeds above a time-dependent inhomogeneous background as well.

Remarks on a nonlinear electromagnetic extension in AdS Reissner-Nordström spacetime

We explore the gravitational properties of a nonlinear electromagnetic extension of an AdS Reissner-Nordström black hole. Our study begins with an analysis of the metric function and horizon structure, followed by calculations of the Ricci and Kretschmann scalars and an evaluation of the non-vanishing Christoffel symbols. These calculations allow us to examine geodesics and their influence on the photon sphere and shadow formation. In the thermodynamic framework, we evaluate essential quantities, including the Hawking temperature, entropy, heat capacity, Gibbs free energy, and Hawking radiation emission. We further investigate black hole evaporation by estimating the evaporation timescale as the black hole approaches its final state. Additionally, quasinormal modes for scalar and vector perturbations are computed using the WKB approximation to characterize oscillatory behavior of the system. Finally, a time-domain analysis is provided in order to examine the evolution of these perturbations.

Effect of energetic ions on edge-localized modes in tokamak plasmas

The most efficient and promising operational regime for the International Thermonuclear Experimental Reactor tokamak is the high-confinement mode. In this regime, however, periodic relaxations of the plasma edge can occur. These edge-localized modes pose a threat to the integrity of the fusion device. Here we reveal the strong impact of energetic ions on the spatio-temporal structure of edge-localized modes in tokamaks using nonlinear hybrid kinetic–magnetohydrodynamic simulations. A resonant interaction between the fast ions at the plasma edge and the electromagnetic perturbations from the edge-localized mode leads to an energy and momentum exchange. Energetic ions modify, for example, the amplitude, frequency spectrum and crash timing of edge-localized modes. The simulations reproduce some observations that feature abrupt and large edge-localized mode crashes. The results indicate that, in the International Thermonuclear Experimental Reactor, a strong interaction between the fusion-born alpha particles and ions from neutral beam injection, a main heating and fast particle source, is expected with predicted edge-localized mode perturbations. This work advances the understanding of the physics underlying edge-localized mode crashes in the presence of energetic particles and highlights the importance of including energetic ion kinetic effects in the optimization of edge-localized mode control techniques and regimes that are free of such modes.

Magneto Dynamic Stability of Bounded Cylindrical Streaming Fluid Jet Pervaded by Toroidal Magnetic Field

The hydromangetic stability of bounded fluid jet under the influence of the electromagnetic (with toroidal varying field) force has been developed. A general dispersion relation valid for all modes of perturbation is derived. The geometric factor q which is the radii ratio of the tenuous-fluid regions plays an important role for stabilizing the model. The axial and transvers magnetic fields interior and exterior the fluid jet are stabilizing. The magnetic fields decrease the streaming destabilizing domains and at the same time give a sort or rigidity to the fluid molecules. For any value of the applying magnetic field strength, the instability character of the streaming model could be suppressed and dispersed. These results are confirmed numerically upon using computer programs.

Predicting spatial curvature ΩK in globally CPT -symmetric universes

Boyle and Turok’s CPT-symmetric universe model posits that the Universe was symmetric at the big bang, addressing numerous problems in both cosmology and the Standard Model of particle physics. We extend this model by incorporating the symmetric conditions at the end of the Universe, which impose constraints on the allowed perturbation modes. These constrained modes conflict with the integer wave vectors required by the global spatial geometry in a closed universe. To resolve this conflict, only specific values of curvature are permissible, and in particular the curvature density is constrained to be ΩK∈{−0.016,−0.011,−0.004,…}, consistent with observations. Published by the American Physical Society 2024

Interplay of the magnetic and current density field topologies in axisymmetric devices for magnetic confinement fusion

In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile $q=q_{\boldsymbol {B}}$ . A corresponding profile, $q_{\boldsymbol {J}}$ , can be defined for the current density field lines. Ampère's law relates any mode of current perturbation $\delta \boldsymbol {J}_{m,n}$ with a mode of magnetic perturbation $\delta \boldsymbol {B}_{m,n}$ . It is shown that the knowledge of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ allows us then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of $q_{\boldsymbol {J}}$ in the flux coordinate is derived. Including this calculation in real-time Grad–Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ would then allow us to investigate the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of $q_{\boldsymbol {B}}$ and $q_{\boldsymbol {J}}$ are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated with magnetic islands but with non-resonant magnetic modes. It remains to be explored to what extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial.

Stability of Cauchy horizon in Einstein–Power–Maxwell–de Sitter black holes

We investigated the Strong Cosmic Censorship (SCC) conjecture in Einstein–Power–Maxwell–de Sitter (EPMdS) black holes by analyzing the quasinormal modes (QNMs) of a massless neutral scalar field perturbation. Using the pseudospectral method, we calculated the QNM frequencies across various cosmological constants and nonlinear electromagnetic parameters. Our results show that for black holes far from extremality, the lowest QNM frequency -Im(ω)/κ- remains below 1/2. However, as the black holes approach extremality, the lowest mode’s -Im(ω)/κ- consistently exceeds 1/2, leading to a violation of SCC. Moreover, with a fixed cosmological constant, as the nonlinearity parameter α increases, the interval of SCC violation under the charge extremality ratio narrows. Considering that k=1/2+1/α is inversely proportional to α, our results indicate that increasing the order k of the non-linear electromagnetic field can effectively mitigate SCC violations.

Charged black holes with Yukawa potential

This study derives a novel family of charged black hole solutions featuring short- and long-range modifications. These are achieved through a Yukawa-like gravitational potential modification and a nonsingular electric potential incorporation. The short-range corrections encode quantum gravity effects, while the long-range adjustments simulate gravitational effects akin to those attributed to dark matter. Our investigation reveals that the total mass of the black hole undergoes corrections owing to the apparent presence of dark matter mass and the self-adjusted electric charge mass. Two distinct solutions are discussed: a regular black hole solution characterizing small black holes, where quantum effects play a crucial role, and a second solution portraying large black holes at considerable distances, where the significance of Yukawa corrections comes into play. Notably, these long-range corrections contribute to an increase in the total mass and hold particular interest as they can emulate the role of dark matter. Finally, we explore the phenomenological aspects of the black hole. Specifically, we examine the influence of electric charge and Yukawa parameters on thermodynamic quantities, the quasinormal modes for the charged scalar perturbations as well as for the vector perturbations, analysis of the geodesics of light/massive particles, and the accretion of matter onto the charged black hole solution.

Primordial Perturbations Including Second-Order Derivatives of the Inflationary Potential

In inflationary cosmology, the form of the potential is still an open problem. In this work, second-order effects of the inflationary potential are evaluated and related to the known formula for the primordial perturbations at a wide range of scales. We found effects that may help to unravel the unknown inflationary potential form and impose new constraints on the parameters that define this potential. In particular, we demonstrate that even slight deviations in the inflationary potential can lead to significant differences in the calculated spectra if inflation persists sufficiently long and the normal modes of perturbations are affected by these variations.

Analytical calculation of the kinetic q factor and resonant response of toroidally confined plasmas

Symmetry-breaking perturbations in axisymmetric toroidal plasma configurations have a drastic impact on particle, energy, and momentum transport in fusion devices, thereby affecting their confinement properties. The perturbative modes strongly affect particles with specific kinetic characteristics through resonant mode–particle interactions. In this work, we present an analytical calculation of the kinetic q factor, enabling the identification of particles with kinetic properties that meet the resonant conditions. This allows us to predict the locations and structures of the corresponding resonant island chains, as well as the existence of transport barriers in the particle phase space. The analytical results, derived for the case of a large aspect ratio configuration, are systematically compared to numerical simulations, and their domain of validity is thoroughly investigated and explained. Our findings demonstrate that calculating the kinetic q factor and its dependence on both particle and magnetic field characteristics provides a valuable tool for understanding and predicting the resonant plasma response to non-axisymmetric perturbations. Moreover, this approach can be semi-analytically applied to generic realistic experimental equilibria, offering a low-computational-cost method for scenario investigations under various multi-scale perturbative modes.

Analytical QNMs of fields of various spin in the Hayward spacetime

By employing an expansion in terms of the inverse multipole number, we derive analytic expressions for the quasinormal modes (QNMs) of scalar, Dirac and Maxwell perturbations in the Hayward black hole (BH) background. The metric has three interpretations: as a model for a radiating BH, as a quantum-corrected BH owing to the running gravitational coupling in the Asymptotically Safe Gravity, and as a BH solution in the Effective Field Theory. We show that the obtained compact analytical formulas approximate QNMs with remarkable accuracy for ℓ > 0.

Homo-Site Nucleation Growth of Twisted Bilayer MoS2 with Commensurate Angles.

Moiré superlattices, composed of two layers of transition metal dichalcogenides with a relative twist angle, provide a novel platform for exploring the correlated electronic phases and excitonic physics. Here, a gas-flow perturbation chemical vapor deposition (CVD) approach is demonstrated to directly grow MoS2 bilayer with versatile twist angles. It is found that the formation of twisted bilayer MoS2 homostructures sensitively depends on the gas-flow perturbation modes, correspondingly featuring the nucleation sites of the second layer at the same (homo-site) as or at the different (hetero-site) from that of the first layer. The commensurate twist angle of ≈22° in homo-site nucleation strategy accounts for ≈16% among the broad range of twist angles due to its low formation energy, which is in consistence with the theoretical calculation. More importantly, moiré interlayer excitons with the enhanced photoluminescence (PL) intensity and the prolonged lifetime are evidenced in the twisted bilayer MoS2 with a commensurate angle of 22°, which is owing to the reason that the strong moiré potential facilitates the interlayer excitons to be trapped in the moiré superlattices. The work provides a feasible route to controllably built twisted MoS2 homostructures with strong moiré potential to investigate the correlated physics in twistronics systems.

Towards a momentum potential theory for reacting flows

Mutual coupling of (thermofluiddynamic) modes of perturbations can affect the thermo-acoustic stability of combustors and contribute to combustion noise. For example, vortical or entropic perturbations can be transferred to acoustic perturbations if accelerated by the mean flow. The decomposition of perturbation fields into the respective modes and a linear description of their interactions in terms of fluctuating primitive variables is challenging. In contrast, Doak’s momentum potential theory promises an unambiguous decomposition in terms of momentum fluctuations, which is not limited to the linear regime. Whereas classical momentum potential theory takes into account hydrodynamic, acoustic and entropic modes in unconfined flows, the investigation of noise generation in combustion chambers requires the extension of the momentum potential theory to capture modes linked to the fluctuation of species mass fractions (“species mode”) arising from the change in chemical composition due to the reaction. Furthermore, a rigorous treatment of boundary conditions due to the confinement of the flow inside the combustor is required. The herein presented extension to reactive flows consists of two steps, (i) the formulation of a potential for momentum fluctuations related to species modes and (ii) identification of the total fluctuating enthalpy related to species modes. The extended theory is applied to post-process computational fluid dynamic simulation data of the propagation of entropy and species perturbations through one-dimensional ducts, nozzles and premixed flames. We find that although momentum potential theory offers a complete decomposition of momentum perturbations for reactive flows, the meaningful interpretation of this decomposition is rather challenging, even for non-reactive flows.

On the stability of vortex quantum droplets

We discuss the stability of topological quantum droplets with the shape of two-dimensional soliton rings endowed with angular momentum that stem from a symmetric binary mixture in a Bose–Einstein condensate, with a strong trapping in one of the three spatial dimensions. We show that, in the lossless symmetric case, modeled by a Schrödinger equation with a Shannon-type nonlinear potential function, stable eigenstates can exist for arbitrarily large values of their topological charge l, provided the number of atoms is above a certain threshold. By comprehensive numerical computations, we analyze in detail cases up to l=50. We have found the perturbation modes and their eigenvalues, determining in each case which one dominates and destabilizes the solutions that lie below the stability threshold. We compare these results to the fate of the eigenstates that evolve in time. We also study the stability of the droplets under dynamical conditions by simulating collisions with potential barriers.

Quasinormal modes of the Schwarzschild black hole with a deficit solid angle and quintessence-like matter: improved asymptotic iteration method

We study the quasinormal modes (QNMs) for scalar and electromagnetic perturbations in the Schwarzschild black hole with a deficit solid angle and quintessence-like matter. Using the sixth-order WKB approximation and the improved asymptotic iteration method, we can determine the dependence of the QNMs on the parameters of the black hole and the parameters on the test fields. The values of the real part and imaginary parts of the QNMs increase with the decrease of the values of the deficit solid angle and density of quintessence-like matter. The QNMs gotten by these two methods are in good agreement. Using the finite difference method, we obtain the time evolution profile of such perturbations in this black hole.

Causality and quasi-normal modes in the GREFT

The General Relativity Effective Field Theory (GREFT) introduces higher-derivative interactions to parameterise the gravitational effects of massive degrees of freedom which are too heavy to be probed directly. The coefficients of these interactions have recently been constrained using causality: both from the analytic structure of 4-point graviton scattering and the time delay of gravitational waves on a black hole background. In this work, causality is used to constrain the quasi-normal mode spectrum of GREFT black holes. Demanding that quasi-normal mode perturbations decay faster in the GREFT than in General Relativity—a new kind of causality condition which stems from the analytic structure of 2-point functions on a black hole background—leads to further constraints on the GREFT coefficients. The causality constraints and compact expressions for the GREFT quasi-normal mode frequencies presented here will inform future parameterised gravitational waveforms, and the observational prospects for gravitational wave observatories are briefly discussed.

Rapid Normal Stress Oscillations Cause Weakening and Anelastic Dilation in Gouge‐Bearing Faults

AbstractFault normal stress (σn) changes dynamically during earthquakes. However, the impact of these changes on fault strength is poorly understood. We explore the effects of rapidly varying σn by conducting rotary‐shear experiments on simulated fault gouges at 1 μm/s, under well‐drained, hydrothermal conditions. Our results show both elastic and anelastic (time‐dependent but recoverable) changes in gouge layer thickness in response to step changes and sinusoidal oscillations in σn. In particular, we observe dilation associated with marked weakening during ongoing σn‐oscillations at frequencies >0.1 Hz. Moreover, recovery of shear stress after such oscillations is accompanied by transient (anelastic) compaction. We propose a microphysically based friction model that explains most of the observations made, including the effects of temperature and step versus sinusoidal perturbation modes. Our results highlight that σn‐oscillations above a specific frequency threshold, controlled by the loading regime and frictional properties of the fault, may enhance seismic hazards.

Unstable buoyant viscoelastic fluid flow in a vertical porous layer with temperature-dependent viscosity

The stability of thermally driven buoyant flow of a viscoelastic fluid saturating a vertical porous layer with viscosity depending linearly on temperature is investigated numerically. The rheological behavior of the fluid is described through the Oldroyd-B model, leading to a modified Darcy's law of momentum transfer in the porous medium. The study explores the linear stability of the base flow by analyzing the behavior of normal modes of perturbation. Neutral stability curves and the critical Darcy–Rayleigh number are determined for a wide range of viscoelastic and viscosity parameters. Transition curves from stability to instability in the viscoelastic parameters space are also provided for both constant and variable viscosity cases. Additionally, the results for Newtonian, Boger, and Maxwell fluids are delineated as particular cases from this study.

The stability and morphology of laminar premixed hydrogen/air flames under various gravity conditions

In the present work, direct numerical simulations (DNS) were employed to understand the stability and morphology of laminar lean premixed hydrogen/air flames under various gravity conditions. The combined effect of Darrieus–Landau (DL) instability, thermal-diffusive (TD) instability and Rayleigh–Taylor (RT) instability was studied quantitatively for both the initial linear regime and the long-term nonlinear regime, with a particular focus on the effect of RT instability. In the linear regime, it was found that the RT instability has a negligible effect on the linear growth rate of flames with an equivalence ratio of 0.4, but the effect is significant when the equivalence ratio decreases to 0.3. The performance of various models for the dispersion relation was discussed, including a theoretical model considering the effects of all instabilities, which captures well the trend of the simulated results in the cases with unity Lewis numbers. The hydrogen/air flames with an equivalence ratio of 0.3 was investigated comprehensively in the nonlinear regime. For the cases with unity Lewis numbers, the RT-unstable flame exhibits a similar single-cusp structure as the RT-neutral flame, but with a deeper cusp and larger consumption speed as a result of the destabilizing effect of RT instability. The RT-stable flame gradually returns to a planar flame shape owing to the stabilizing effect of RT instability. For the cases with non-unity Lewis numbers, the effect of domain size on the flame evolution was investigated, showing a domain width of 200δT is enough to obtain a domain-independent result, where δT is the laminar flame thickness. It was found that the cases initialized with multimode perturbations reach the quasi-steady state faster, while the flame statistics are consistent with those of the cases initialized with single mode perturbations. The effect of RT instability was explored by comparing the results from various gravity conditions. The flame consumption speed is the largest in RT-unstable flames, and the smallest in RT-stable flames. The variation in flame consumption speed is due to the difference in the flame surface area, while the local reactivity and flame structure are not influenced by the RT instability. Further fractal analysis reveals that although the RT instability causes significant differences in flame surface area, the characteristic fractal dimension remains constant for flames under different gravity conditions.Novelty and significanceIn the present work, direct numerical simulations were employed to understand the stability and morphology of RT-unstable, RT-neutral and RT-stable laminar lean premixed hydrogen/air flames. For the first time, the effect of DL, TD and RT instabilities was quantitatively examined for both the linear regime and the nonlinear regime. A theoretical model considering various instabilities was compared with the simulated dispersion relations in the linear regime. In the non-linear regime, the flame surface area and corresponding flame consumption speed are influenced by the RT instability, while the flame stretch factor remains unaffected. A fractal analysis was conducted in laminar premixed hydrogen/air flames under the influence of various instabilities. Remarkably, it was discovered that the characteristic fractal dimension remains constant for the cases with and without the RT instability.