Gravitational Modes Research Articles

Radiative and gravitating modes in the partially ionized magnetized dusty plasma

In the present study, fluid theory is used to investigate the gravitational and radiative condensation instabilities of a partially ionized magnetized dusty plasma system. The effects of ion and electron capture by dust grains, the charge variation of dust grains, and the radiative effects of electron species are also taken into account. The dynamics of all four species are considered to derive modified densities that further lead to a general dispersion relation. The general dispersion relation describes the propagation of low frequency electrostatic dust acoustic waves in magnetized self-gravitating partially ionized dusty plasma with ionization-recombination, dust charge variations, and radiative effects. Gravitational modes of propagation and radiative modes of propagation are illustrated separately for both parallel and perpendicular cases. Conditions for instabilities are also derived to explain the gravitational collapse and radiative condensation of the system. The numerical results are presented to signify the role of dust neutral collision frequency, dust charge fluctuation, magnetic field, and recombination ionization effects on both the radiative condensation and gravitational instabilities. The relevance of the present study to interstellar molecular clouds is also discussed and the effect of considered parameters on the critical wavelength, critical wave number, luminosity, etc., has been investigated.

On the Mantle‐Inner Core Gravitational Oscillation Under the Action of the Electromagnetic Coupling Effects

AbstractPrevious works indicated that the eigenperiod of the mantle‐inner core gravitational coupling mode can match the observed 6‐year period in length‐of‐day. However, this mode is only an ideal model, since it does not involve the electromagnetic (EM) coupling effects. Here, we further study the mantle‐inner core gravitational mode and its mathematical equation under the action of the EM coupling effects, while the relevant damping oscillation analytical solution is also given. According to this theoretical model, we can constrain the core‐mantle gravitational coupling strength Γ (>6.5 × 1019 Nm) and infer the EM coupling information at the core‐mantle boundary (CMB) and the inner core boundary. This work indicates that a partial liquid core is necessarily required to be coupled to the inner core (IC) and axially rotates with the IC as a single body, which supports the recent assumption that only a part fluid core within the so‐called tangent cylinder is locked to the IC. This explanation can greatly weaken the perturbation magnetic field due to the shear oscillation at the inner core boundary and eliminate the relevant EM damping dissipation, otherwise, the predicted 6‐year oscillation will be rapidly decayed with a relaxation time ~9.8 days. In addition, we give the physical expression of the theoretical quality factor Q value of the 6‐year oscillation, which is mainly related to the EM coupling at the CMB. According to the typical EM coupling parameters at the CMB, the theoretical Q value is predicted in the range of 40–75, which coincides with the current observed result (~51.6).

Multipolar effective one body model for nonspinning black hole binaries

We introduce \TEOBiResumSM{}, a nonspinning inspiral-merger-ringdown waveform model built within the effective one body (EOB) framework that includes gravitational waveform modes beyond the dominant quadrupole $(\ell,|m|) = (2,2)$. The model incorporates: (i) an improved Pad\'e resummation of the factorized waveform amplitudes $\rho_{\ell m}^{\rm orb}$ entering the EOB-resummed waveform where the 3PN, mass-ratio dependent, terms are hybridized with test-mass limit terms up to 6PN relative order for most of the multipoles up to $\ell=6$ included; (ii) an improved determination of the effective 5PN function $a_6^c(\nu)$ entering the EOB interaction potential done using the most recent, error-controlled, nonspinning numerical relativity (NR) waveforms from the Simulating eXtreme Spacetimes (SXS) collaboration; and (iii) a NR-informed phenomenological description of the multipolar ringdown. Such representation stems from 19 NR waveforms with mass ratios up to $m_1/m_2=18$ as well as test-mass waveform data, although it does not incorporate mode-mixing effects. The NR-completed higher modes through merger and ringdown considered here are: $(\ell,|m|) = \lbrace (2,1), (3,3), (3,2),(3,1),(4,4), (4,3),(4,2), (4,1),(5,5)\rbrace$. For simplicity, the other subdominant modes, up to $\ell=8$, are approximated by the corresponding, purely analytical, factorized and resummed EOB waveform. To attempt an estimate of (some of) the underlying analytic uncertainties of the model, we also contrast the effect of the 6PN-hybrid Pad\'e-resummed $\rho_{\ell m}$'s with the standard $3^{+2}$PN, Taylor-expanded, ones used in previous EOB works. The maximum unfaithfulness $\bar{F}$ against the SXS waveforms including all NR-completed modes up to $\ell=m=5$ is always $\lesssim 2\%$ for binaries with total mass $M$ as $50 M_{\odot} \leq M \lesssim 200 M_{\odot}$.

Stabilization of the Gravitational Orientation Mode of an Artificial Earth Satellite (AES) by the Electromagnetic Control System

The possibility of stabilizing the gravitational orientation mode of a massive artificial Earth satellite (AES) by the torque produced by electromagnets interacting with Earth’s magnetic field is shown. As an example, the control of rotational motion of the satellite like Bion M-1 and Foton M-4 is considered. Control is accomplished by changing the currents in the electromagnets. The control law is considered, which provides damping of the disturbed motion of a satellite and its stabilization in the gravitational orientation mode. To form this law, it is sufficient to have the readings of a triaxial magnetometer and of an angular velocity sensor. The control law efficiency is verified by mathematically modeling satellite motion relative to the center of masses, under an effect of gravitational and aerodynamic torques, as well as the torque produced by electromagnets.

Quasinormal modes of black holes. II. Padé summation of the higher-order WKB terms

In previous work [1] we proposed an improvement of the WKB-based semianalytic technique of Iyer and Will for calculation of the quasiormal modes of black holes by constructing the Pad\'e approximants of the formal series for $\omega^{2}.$ It has been demonstrated that (within the domain of applicability) the diagonal Pad\'e transforms $\mathcal{P}_{6}^{6}$ and $\mathcal{P}_{7}^{6}$ are always in a very good agreement with the numerical results. In this paper we present a further extension of the method. We show that it is possible to reproduce many known numerical results with a great accuracy (or even exactly) if the Pad\'e transforms are constructed from the perturbative series of a really high order. In our calculations the order depends on the problem but it never exceeds 700. For example, the frequencies of the gravitational mode $l=2,$ $n=0$ calculated with the aid of the Pad\'e approximants and within the framework of the continued fractions method agree to 24 decimal places. The use of such a large number of terms is necessary as the stabilization of the quasinormal frequencies can be slow. Our results reveal some unexpected features of the WKB-based approximations and may shed some fresh light on the problem of overtones.

Modifications to Plane Gravitational Waves from Minimal Lorentz Violation

General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found.

Gravitational edge modes: from Kac–Moody charges to Poincaré networks

We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together through their interfaces, we focus on a single domain and its punctured 2D boundary. The punctures carry a ladder of Kac–Moody edge modes, whose 0-modes represent the electric and momentum charges while the higher modes describe the stringy vibration modes of the 1D-boundary around each puncture. In particular, this allows to identify missing observables in the discretization scheme used in loop quantum gravity (LQG) and leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. In the limit where the tubes are contracted to 1D links and the string modes neglected, we do not just recover LQG but obtain a more general structure: Poincaré charge networks, which carry a representation of the 3D diffeomorphism boundary charges on top of the fluxes and gauge transformations.

Localized gravitons as essence of dark energy: Implications for accelerated cosmic expansion

A theory of Emerging Quantum Mechanics (EQM) has been developed [1] con-tributing to the understanding of the measurement problem by assigning a quantum dynamical process to collapse within Schrödinger’s theory.EQM treats cosmological problems in a quantum field theory in high dimensional spacetime (11D) including matter and the gravitational field. Gravity is quantized in the weak interaction limit. The EQM Lagrangian contains terms up to fourth order in the gravitational field. Second and fourth order terms are associated with repulsive dark energy and third order terms with attractive dark matter effects. Gravonon-gravonon repulsion, i.e. dark energy in EQM, modifies the structure of the gravitational field and leads to accelerated expansion of the universe.Quantum diffusion of the matter particles in three dimensional space is suggested as the mechanism of the expansion of the universe. The rate of expansion is given by the frequency of the soft gravitational modes. A lower limit of the deceleration parameter for the expansion of the universe, derived in EQM, is in the range between -0.6 and -0.8, an observed value of -0.55 has been reported.

Analysis of radiative gravitational modes in magnetized dusty plasma with non-thermal ion distribution

The characteristics of radiative gravitational modes in non-thermal magnetized dusty plasma with charge fluctuation and the polarization force of dust particles are investigated. The electron species are assumed to be radiative and the ions are assumed to be non-thermal. A normal mode analysis is applied to derive the general dispersion relation for radiative magnetized self-gravitating dusty plasma. Modified radiative condensation and self-gravitational instability criteria for both perpendicular and parallel modes of propagation are obtained. Analytically, it is found that the presence of a non-thermal ion population significantly modified the usual radiative condensation instability criterion, and damped the growth rate of the radiative mode. The obtained analytical results are further discussed in the numerical result section. We investigate the fact that the non-thermal ion population acts as a stabilizing source for radiative condensation instability in magnetized self-gravitating dusty plasma fluid, including the dust polarization force and charge fluctuation. The thermal conductivity with non-thermal ion distribution quickly moves the system towards stability. The implications of the results in the region of the interstellar medium (ISM) are discussed.

Radiative and Gravitational Modes and Instabilities in an Inhomogeneous Magneto Dusty Plasma with Charge Variation

The Jeans instability of collisional magnetized dusty plasmas is examined incorporating polarization force, charge variation of dust grains, and radiative cooling of ion and electron species. The collisional effects of dust grains with neutrals are considered with sufficient background of neutral particles. A general dispersion relation is obtained using normal mode analysis technique which is found to be modified due to polarization force, dust charge fluctuation, and radiative effects of electrons and ions. The analytical discussion of general dispersion relation is presented in parallel and perpendicular mode of propagation. The Routh Hurwitz criterion is applied to analyze the stability of the considered system. We report the existence of a modified cyclotron mode in parallel propagation and a purely collisional mode in perpendicular propagation along with the gravitational mode. These modes are discussed analytically, as well as numerically, to show the importance of different parameters considering different situations. The implications of the result have been discussed for the molecular clouds.

Synchrosqueezing transforms: From low- to high-frequency modulations and perspectives

The general aim of this paper is to introduce the concept of synchrosqueezing transforms (SSTs) that was developed to sharpen linear time–frequency representations (TFRs), like the short-time Fourier or the continuous wavelet transforms, in such a way that the sharpened transforms remain invertible. This property is of paramount importance when one seeks to recover the modes of a multicomponent signal (MCS), corresponding to the superimposition of AM/FM modes, a model often used in many practical situations. After having recalled the basic principles of SST and explained why, when applied to an MCS, it works well only when the modes making up the signal are slightly modulated, we focus on how to circumvent this limitation. We then give illustrations in practical situations either associated with gravitational wave signals or modes with fast oscillating frequencies and discuss how SST can be used in conjunction with a demodulation operator, extending existing results in that matter. Finally, we list a series of different perspectives showing the interest of SST for the signal processing community.

General Assertions on the Gravitational Waves Polarization Modes from an f(R) Model of Gravity

Detailed analysis of an f( R) theory is emphasized in a Minkowski and non trivial background. It is shown that the polarization modes depend strongly on the metric or Palatini formalism, Einstein or Jordan frame, function f (R ), background gravitational field and the observer.

Gravitational wave driving of a gapped holographic system

This work addresses the response of a holographic conformal field theory to a homogeneous gravitational periodic driving. The dual geometry is the AdS-soliton, which models a strongly coupled quantum system in a gapped phase, on a compact domain. The response is a time-periodic geometry up to a driving amplitude threshold which decreases with the driving frequency. Beyond that, collapse to a black hole occurs, signaling decoherence and thermalization in the dual theory. At some frequencies, we also find a resonant coupling to the gravitational normal modes of the AdS-soliton, yielding a nonlinearly bound state. We also speculate on the possible uses of quantum strongly coupled systems to build resonant gravitational wave detectors.

Primordial gravitational waves in Horndeski gravity

We investigate the propagation of primordial gravitational waves within the context of the Horndeski theories, for this, we present a generalized transfer function quantifying the sub-horizon evolution of gravitational waves modes after they enter the horizon. We compare the theoretical prediction of the modified primordial gravitational waves spectral density with the aLIGO, Einstein telescope, LISA, gLISA and DECIGO sensitivity curves. Assuming reasonable and different values for the free parameters of the theory (in agreement with the event GW170817 and stability conditions of the theory), we note that the gravitational waves amplitude can vary significantly in comparison with general relativity. We find that in some cases the gravitational primordial spectrum can cross the sensitivity curves for DECIGO detector with the maximum frequency sensitivity to the theoretical predictions around 0.05 - 0.30 Hz. From our results, it is clear that the future generations of space based interferometers can bring new perspectives to probing modifications in general relativity.

Gravitational axial perturbations and quasinormal modes of loop quantum black holes

Loop quantum gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole’s singularity. The detection of gravitational waves, on the other hand, has opened the way to new perspectives in the investigation of the spacetime structure. In this work, by the use of a WKB method introduced by Schutz and Will (Astrophys J 291:L33, 1985), and after improved by Iyer and Will (Phys Rev D 35:3621, 1987), we study the gravitational wave spectrum emitted by loop quantum black holes, which correspond to a quantized version of the Schwarzschild spacetime by LQG techniques. From the results obtained, loop quantum black holes have been shown stable under axial gravitational perturbations.

Unknown branch of the total-transmission modes for the Kerr geometry

The gravitational modes of the Kerr geometry include both quasinormal modes and total-transmission modes. Sequences of these modes are parameterized by the angular momentum of the black hole. The quasinormal and total-transmission modes are usually distinct, having mode frequencies that are different at any given value of the angular momentum. But a discrete and countably infinite subset of the left-total-transmission modes are simultaneously quasinormal modes. Most of these special modes exist along previously unknown branches of the gravitational total-transmission modes. In this paper, we give detailed plots of the total-transmission modes for harmonic indices $\ell=[2,7]$, with special emphasis given to the $m=0$ modes which all contain previously unknown branches. All of these unknown branches have purely imaginary mode frequencies. We find that as we approach the Schwarzschild limit along these new branches, the mode frequencies approach $-i\infty$ in stark contrast to the finite mode frequency obtained in the Schwarzschild limit along the previously known branches. We explain when and why, at certain frequencies, the left-total-transmission modes are simultaneously quasinormal modes. At these same frequencies, the right-total-transmission modes are missing. We also derive analytic expressions for the asymptotic behavior of the total-transmission mode frequencies, and for the values of the angular momentum at which the modes are simultaneously quasinormal modes.

Гравитационная ориентация транспортных грузовых кораблей Прогресс МС-07 и Прогресс МС-08

Гравитационная ориентация транспортных грузовых кораблей Прогресс МС-07 и Прогресс МС-08

Propagation of gravitational waves in teleparallel gravity theories

We investigate propagation of gravitational waves in the most general teleparallel gravity model with second order field equations around the Minkowski background. We argue that in this case the most general Lagrangian at the first order of perturbations is given by the linear combination of quadratic invariants and hence coincides with the well-known new general relativity model. We derive the linearized field equations and analyze them using the principal polynomial and the Newman-Penrose formalism. We demonstrate that all gravitational wave modes propagate at the speed of light and there are up to six possible polarizations. We show that two tensorial modes of general relativity are always present and the number of extra polarizations depends on the free parameters of the new general relativity model.

Oscillation modes of hybrid stars within the relativistic Cowling approximation

The first direct detection of gravitational waves has opened a new window to study the Universe and would probably start a new era: the gravitational wave Astronomy. Gravitational waves emitted by compact objects like neutron stars could provide significant information about their structure, composition and evolution. In this paper we calculate, using the relativistic Cowling approximation, the oscillations of compact stars focusing on hybrid stars, with and without a mixed phase in their cores. We study the existence of a possible hadron-quark phase transition in the central regions of neutron stars and the changes it produces on the gravitational modes frequencies emitted by these stars. We pay particular attention to the g-modes, which are extremely important as they could signal the existence of pure quark matter inside neutron stars. Our results show a relationship between the frequency of the g-modes and the constant speed of sound parametrization for the quark matter phase. We also show that the inclusion of color superconductivity produces an increase on the oscillation frequencies. We propose that observations of g-modes with frequencies fg between 1 kHz and 1.5 kHz should be interpreted as an evidence of a sharp hadron-quark phase transition in the core of a compact object.

Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes

Einstein-Maxwell-dilaton theory is an interesting and well-motivated theoretical laboratory to explore the impact of new fundamental degrees of freedom in the context of testing the no-hair conjecture, due to the existence of hairy black hole solutions together with the propagation of scalar, vector and tensor modes. In this paper we compute the quasinormal mode spectrum of static and slowly rotating black holes for generic values of the dilaton coupling, within a weak electric charge approximation. Our results suggest that these spacetimes are stable for generic values of the dilaton coupling and the black hole charge. We also show that while gravitational modes are only weakly affected by the coupling with the dilaton, the spectrum of electromagnetic modes exhibits a more pronounced dilaton-dependent breaking of isospectrality between the axial and polar sectors. We further show that the gravitational quasinormal modes are well approximated by the properties of unstable null circular geodesics in those spacetimes, while the treatment of electromagnetic and scalar modes can be simplified by a suitably modified Dudley-Finley scheme for the perturbed equations.