Interaction Of Gravitational Waves Research Articles

Interaction of gravitational waves with Yang–Mills fields

Interaction of gravitational waves with Yang–Mills fields

Path Integral Action for a Resonant Detector of Gravitational Waves in the Generalized Uncertainty Principle Framework

The Heisenberg uncertainty principle is modified by the introduction of an observer-independent minimal length. In this work, we have considered the resonant gravitational wave detector in the modified uncertainty principle framework, where we have used the position momentum uncertainty relation with a quadratic order correction only. We have then used the path integral approach to calculate an action for the bar detector in the presence of a gravitational wave and then derived the Lagrangian of the system, leading to the equation of motion for the configuration-space position coordinate in one dimension. We then find a perturbative solution for the coordinate of the detector for a circularly polarized gravitational wave, leading to a classical solution of the same for the given initial conditions. Using this classical form of the coordinate of the detector, we finally obtain the classical form of the on-shell action describing the harmonic oscillator–gravitational wave system. Finally, we have obtained the free particle propagator containing the quantum fluctuation term considering gravitational wave interaction.

Interaction of gravitational waves with permeable breakwater

A method for calculating the parameters of gravitational waves that interact with vertical permeable breakwaters, based on potential theory, has been developed and presented. The wave motion of a fluid was described by the velocity potential that satisfies the Laplace equation. The shape of the wave surface and the components of the velocity vector were determined. Numerical analysis of the influence of permeability of the vertical wall on wave energy adsorption was carried out. The propagation of surface gravitational waves in the linear formulation of problems in a channel with a vertical permeable obstacle was analyzed. The dependence of the wave reflection coefficient as a function of the wave transmission coefficient in accordance with the law of energy conservation was given. Experimental studies have been conducted to determine the features of the hydrodynamic interaction of sea waves and coastal protection structures of the permeable type. The experiments were performed in the laboratory in a wave channel with models of vertical slotted walls of different permeability. Visual and instrumental studies have shown the features of the interaction of the wave field with permeable breakwaters, the formation of reflection and transmission waves through the breakwater. It is established that vertical slotted walls, depending on the permeability, significantly affect the wave field, generate reflected waves and waves passing through the breakwater, as well as lead to a significant dissipation of wave energy. The dependences of the reflection and transmission coefficients of the wave, as well as the dissipation coefficient of the wave energy depending on the permeability of the slotted breakwater and the relative depth of the water area were given. It is shown that with increasing permeability of the breakwater the wave reflection coefficient decreased, and the wave transmission coefficient on the contrary increased. It was found that the reflection coefficient of the wave was increased with increasing relative depth, and the coefficient of wave propagation was decreased. The dissipation coefficient of the wave energy had the maximum value, which was observed for greater permeability of the breakwater, when the relative depth compared to the wavelength was increased.

Graviton-photon mixing. Exact solution in a constant magnetic field

In this work I study the effect of graviton-photon mixing in a constant external magnetic field and find for the first time in the literature exact solution of the equations of motion. In particular, I apply the effect of graviton-photon mixing to the case of interaction of gravitational waves with an external magnetic field and calculate the intensity Stokes parameter of the produced electromagnetic radiation. The obtained results are new and extend previous results obtained by using approximation methods.

Dispersion of gravitational waves in cold spherical interstellar medium

We investigate the propagation of locally plane, small-amplitude, monochromatic gravitational waves (GWs) through cold compressible interstellar gas in order to provide a more accurate picture of expected waveforms for direct detection. The quasi-isothermal gas is concentrated in a spherical symmetric cloud held together by self-gravitation. Gravitational waves can be treated as linearized perturbations on the background inner Schwarzschild spacetime. The perturbed quantities lead to the field equations governing the gas dynamics and describe the interaction of gravitational waves with matter. We have shown that the transport equation of these amplitudes provides numerical solutions for the frequency-alteration. The decrease in frequency is driven by the energy dissipating process of GW–matter interactions. The decrease is significantly smaller than the magnitude of the original frequency and too small to be detectable by present second-generation and planned third-generation detectors. It exhibits a power-law relationship between original and decreased frequencies. The frequency deviation was examined particularly for the transient signal GW150914.

The electromagnetic signature of gravitational wave interaction with the quantum vacuum

An analysis of the effects of the passage of a gravitational wave (GW) on the quantum vacuum is made within the context of the Nexus paradigm of quantum gravity. Results indicate that if the quantum vacuum includes electrically charged virtual particle fields, then a GW will induce vacuum polarization. The equations of General Relativity (GR) are then reformulated to include electric charge displacements in the quantum vacuum imposed by an anisotropic stress — momentum tensor. It is then demonstrated that as a result of the spacetime piezoelectric effect, a gravitational wave is associated with a rotating electromagnetic wave and that the converse effect produced by strong electromagnetic fields is responsible for the generation of relativistic jets and gamma ray bursts. Objects with strong electromagnetic fields will apparently violate the strong equivalence principle.

Interaction of gravitational waves with superconductors

Applying the Helmholtz Decomposition theorem to linearized General Relativity leads to a gauge‐invariant formulation where the transverse‐traceless part of the metric perturbation describes gravitational waves in matter. Gravitational waves incident on a superconductor can be described by a linear London‐like constituent equation characterized by a “gravitational shear modulus” and a corresponding plasma frequency and penetration depth. Electric‐like and magnetic‐like gravitational tensor fields are defined in terms of the strain field of a gravitational wave. It is shown that in the DC limit, the magnetic‐like tensor field is expelled from the superconductor in a gravitational Meissner‐like effect. The Cooper pair density is described by the Ginzburg‐Landau theory embedded in curved space‐time. The ionic lattice is modeled by quantum harmonic oscillators coupled to gravitational waves and characterized by quasi‐energy eigenvalues for the phonon modes. The formulation predicts the possibility of a dynamical Casimir effect since the zero‐point energy of the ionic lattice phonons is found to be modulated by the gravitational wave, in a quantum analog of a “Weber‐bar effect.” Applying periodic thermodynamics and the Debye model in the low‐temperature limit leads to a free energy density for the ionic lattice. Lastly, we relate the gravitational strain of space to the strain of matter to show that the response to a gravitational wave is far less for the Cooper pair density than for the ionic lattice. This predicts a charge separation effect in the superconductor as a result of the gravitational wave.

Interaction of gravitational waves with matter from Special Relativity

The predictions of the effective vector formulation of gravitation (GEV), valid for the weak field situation of radiation, are compared to those of General Relativity (GR) for the interaction of gravitational waves with matter. It is shown that their effect is much smaller than what predicted by GR.

Landau's problem in the noncommutative quantum mechanics and linearized gravitational waves: DeWitt's approach

We present a systematic study of the noncommutative interaction of gravitational waves with matter at the quantum mechanical level in the long wavelength and small velocity limit. In particular, the noncommutative quantum dynamics of the Landau's problem is employed to measure the transmission amplitudes in terms of the Riemann's tensor elements by a gravitational wave in linearized approximation. It turns out that the Hamiltonian of the charged particles derived based on DeWitt's approach is valid by the deformed electromagnetic fields.

Interaction of gravitational waves with matter

We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression for the dispersion of gravitational waves in matter in terms of correlation functions for the matter in flat spacetime. The self energy of a gravitational wave is shown to have contributions analogous to the paramagnetic and diamagnetic contributions to the self energy of an electromagnetic wave. We apply the formalism to some simple systems: free particles, an interacting scalar field, and a fermionic superfluid.

Interaction of gravitational waves with magnetic and electric fields

The existence of large-scale magnetic fields in the universe has led to the observation that if gravitational waves propagating in a cosmological environment encounter even a small magnetic field then electromagnetic radiation is produced. To study this phenomenon in more detail we take it out of the cosmological context and at the same time simplify the gravitational radiation to impulsive waves. Specifically, to illustrate our findings, we describe the following three physical situations: (1) a cylindrical impulsive gravitational wave propagating into a universe with a magnetic field, (2) an axially symmetric impulsive gravitational wave propagating into a universe with an electric field and (3) a ``spherical'' impulsive gravitational wave propagating into a universe with a small magnetic field. In cases (1) and (3) electromagnetic radiation is produced behind the gravitational wave. In case (2) no electromagnetic radiation appears after the wave unless a current is established behind the wave breaking the Maxwell vacuum. In all three cases the presence of the magnetic or electric fields results in a modification of the amplitude of the incoming gravitational wave which is explicitly calculated using the Einstein--Maxwell vacuum field equations.

Noncommutative quantum mechanics of a test particle under linearized gravitational waves

We consider the quantum dynamics of a test particle in noncommutative space under the influence of linearized gravitational waves in the long wave-length and low-velocity limit. A prescription for quantizing the classical Hamiltonian for the interaction of gravitational wave with matter in noncommutative space is proposed. The Hamiltonian (and hence the system) is then exactly solved by using standard algebraic methods. The solutions show prominent signatures of the noncommutative nature of space. Computation of the expectation value of the particle's position reveals the inherent quantum nature of spacetime noncommutativity.

Gravitoelectromagnetic cavitons in the kinetic regime

The interactions of gravitational waves with interstellar matter, dealing with resonant wave-particle and wave-wave interactions, are considered on the basis of magnetic-type Maxwell-Vlasov equations. It is found that the behavior of the fields, involving the "gravitoelectromagnetic" or "GEM " fields, the perturbed density field and self-generated gravitomagnetic field with low frequency,can be described by the nonlinear coupling equations Eqs. (6.10)-(6.12). Numerical results show that they may collapse. In other words, due to self-condensing, a stronger GME fields could be produced; and they could appear as the gravitational waves with high energy reaching on Earth. In this case, Weber's results, perhaps, are acceptable.

The damping of gravitational waves in dust

We examine a simple model of the interaction of gravitational waves with matter (primarily represented by dust). The aim is to investigate a possible damping effect on the intensity of the gravitational wave when passing through a medium. This might be important for gravitational wave astronomy when the sources are obscured by dust or molecular clouds.

Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame

We analyze the interaction of the plane `$+$'-polarized gravitational waves with a Fabry-Perot cavity in the local Lorentz frame of the cavity's input mirror outside of the range of long-wave approximation with the force of radiation pressure taken into account. The obtained detector's response signal is represented as a sum of two parts: (i) the phase shift due to displacement of a movable mirror under the influence of a gravitational wave and the force of light pressure, and (ii) the phase shift due to the direct interaction of a gravitational wave with light wave inside the cavity. We obtain the formula for the movable mirror's law of motion paying close attention to the phenomena of optical rigidity, radiative friction, and direct coupling of a gravitational wave to light wave. Some issues concerning the detection of high-frequency gravitational waves and the role of optical rigidity in it are discussed. We also examine in detail special cases of optical resonance and small detuning from it and compare our results with the known ones.

Is it possible to detect gravitational waves with atom interferometers?

We investigate the possibility of using atom interferometers to detect gravitational waves. We discuss the interaction of gravitational waves with an atom interferometer and analyse possible schemes.

Interaction of gravitational waves with strongly magnetized plasmas

We study the interaction of a gravitational wave (GW) with a plasma that is strongly magnetized. The GW is considered a small disturbance, and the plasma is modeled by the general relativistic analogue of the induction equation of ideal MHD and the single fluid equations. The equations are specified to two different cases, first to Cartesian coordinates and a constant background magnetic fields, and second to spherical coordinates together with a background magnetic field that decays with the inverse radial distance. The equations are derived without neglecting any of the nonlinear interaction terms, and the nonlinear equations are integrated numerically. We find that for strong magnetic fields of the order of ${10}^{15}\text{ }\text{ }\mathrm{G}$ the GW excites electromagnetic plasma waves very close to the magnetosonic mode. The magnetic and electric field oscillations have very high amplitude, and a large amount of energy is absorbed from the GW by the electromagnetic oscillations, of the order of ${10}^{23}\text{ }\text{ }\mathrm{erg}/{\mathrm{cm}}^{3}$ in the case presented here, which, when assuming a relatively small volume in a star's magnetosphere as an interaction region, can yield a total energy of at least ${10}^{41}\text{ }\text{ }\mathrm{erg}$ and may be up to ${10}^{43}\text{ }\text{ }\mathrm{erg}$. The absorbed energy is proportional to ${B}_{0}^{2}$, with ${B}_{0}$ the background magnetic field. The energizing of the plasma takes place on fast time scales of the order of milliseconds. Our results imply that the GW-plasma interaction is an efficient and important mechanism in magnetar atmospheres, most prominently close to the star, and, under very favorable conditions though, it might even be the primary energizing mechanism behind giant flares.

The general relativistic magnetohydrodynamic dynamo equation

The magnetohydrodynamic dynamo equation is derived within general relativity, using the covariant 1 + 3 approach, for a plasma with finite electrical conductivity. This formalism allows for a clear division and interpretation of plasma and gravitational effects, and we are not restricted to a particular space‐time geometry. The results should be of interest in astrophysics and cosmology, and the formulation is well suited to gauge-invariant perturbation theory. Moreover, the dynamo equation is presented in some specific limits. In particular, we consider the interaction of gravitational waves with magnetic fields, and present results for the evolution of the linearly growing electromagnetic induction field, as well as the diffusive damping of these fields. Ke yw ords: gravitation ‐ gravitational waves ‐ MHD.

Gravitational waves in plasmas

Various aspects of gravitational wave propagation in plasmas and vacuum are discussed. First, we analyse single particle trajectories, study the resonant interaction of gravitational waves with photons, and show that photons can be strongly energized by gravitational waves. Second, this exchange of energy between the photons and the gravitational waves is treated statistically, using a kinetic equation for photons. Gravitational wave instabilities induced by intense photon beams are considered. The effects are very much dependent on the gravitational wave dispersion in the plasma medium, and in particular, on its turbulent state.

Computational Cosmology: From the Early Universe to the Large Scale Structure.

In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations (and numerical methods applied to specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark-hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.