The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of gravitational waves via a spin-orbit coupling mechanism. We present a covariant derivation from first principles of effective ray equations describing the propagation of polarized gravitational waves, up to first-order terms in wavelength, on arbitrary spacetime backgrounds. The effective ray equations describe a gravitational spin Hall effect for gravitational waves and are of the same form as those describing the gravitational spin Hall effect of light, derived from Maxwell's equations.
In this article, the energy density of plane gravitational wave is studied by using Einstein and Møller's prescription of energy-momentum pseudotensors. The linearly polarized plan gravitational wave solution of Einstein field equation, which has been defined by Bondi et al., is represented by four kinds of different coodrinates. The energy distribution of gravitational wave solution in Einstein and Møller's prescription are obtained. Particularly the energy component is zero in null coordinates.
We discuss polarization of gravitational radiation within the standard framework of linearized general relativity. The recent experimental discovery of gravitational waves provides the impetus to revisit the implications of the spin-rotation-gravity coupling for polarized gravitational radiation; therefore, we consider the coupling of helicity of gravitational waves to the rotation of an observer or the gravitomagnetic field of a rotating astronomical source. Observational possibilities regarding polarization-dependent effects in connection with future gravitational wave detectors are briefly …
Consideration of vacuum polarization in quantum electrodynamics may affect the momentum dispersion relation for photons for a non-trivial background, due to appearance of curvature dependent terms in the effective action. We investigate the effect of a positive cosmological constant $Λ$ on this at one loop order for stationary $Λ$-vacuum spacetimes. To the best of our knowledge, so far it has been shown that $Λ$ affects the propagation in a time dependent black hole spacetime. Here we consider the static de Sitter cosmic string and the Kerr-de Sitter spacetime to show that there can be some no…
We study the observation of polarized stochastic gravitational-wave background (SGWB) in pulsar-timing-array experiments. The time residual for an observed pulsar is formulated as a line-of-sight integral that incorporates the effects of the pulsar term, from which we construct the correlation function of the time residual between a pair of pulsars in terms of the overlap reduction functions (ORFs) for the SGWB intensity and polarization anisotropies. Our formulation provides a numerical scheme for computing the ORFs for high multipole moments and the lowest-moment ORFs for the SGWB linear pol…
The one-loop effective action for QED in curved spacetime contains equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions lead to the dependence of photon velocity on the motion and polarization directions. In this paper we investigate the gravitational analogue to the electromagnetic birefringence phenomenon in the static and radiating topological black hole backgrounds, respectively. For the static topological black hole spacetimes, the velocity shift of photons is the same as the one in the Reissner-Nordström black hole…
Solutions of the linearized Einstein equations are found that describe a transversely confined beam of circularly polarized gravitational waves on a Minkowski backdrop. By evaluating the cycle-averaged stress-energy-momentum pseudotensor of Landau & Lifshitz it is found that the angular momentum density is concentrated in the 'skin' at the edge of the beam where the intensity falls, and that the ratio of angular momentum to energy per unit length of the beam is $2/ω$, where $ω$ is the wave frequency, as expected for a beam of spin-$2$ gravitons. For sharply-defined, uniform, axisymmetric beams…
We investigate the scalar induced gravitational waves (SIGWs) in the Chern-Simons (CS) modified gravity during the radiation dominated era. The SIGWs are circularly polarized, which provide us a tool to test the possible parity violation in the early universe. We derive the semianalytic expressions to evaluate the fractional energy density of the SIGWs, $Ω_{\mathrm{GW}}$, which receives contributions from the general relativity (GR) and the correction due to the parity-violating term, respectively. We find that the degree of the circular polarization of the SIGWs can be as large as of order un…
We investigate the resonant interaction to the weak gravitational waves in a coupling electromagnetic system, which consists of a Gaussian beam with the double polarized transverse electric modes, a static magnetic field and the fractal membranes. We find that under the syncroresonance condition a high-frequency GW (HFGW) of h=10^-30,v_g=3GHz may produce the perturbative photon flux (PPF) of 2.15*10/s in a surface of 0.01m^2. The PPF can be pumped out from the background photon fluxes and one might obtain the amplified signal photon flux of 2.15*10^4s^-1 by cascade fractal membranes. It appear…
We derive a simple relationship between the energy emitted in gravitational waves for a narrowband source and the distance to which that emission can be detected by a single detector. We consider linearly polarized, elliptically polarized, and unpolarized gravitational waves, and emission patterns appropriate for each of these cases. We ignore cosmological effects.
We consider the propagation of gravitational waves generated by slow motion sources in Coulomb type potential due to the mass of the source. Then, the formula for gravitational waveform including tail is obtained in a straightforward manner by using the spherical Coulomb function. We discuss its relation with the formula in the previous work.
The paper gives an introduction to the gravitational radiation theory of isolated sources and to the propagation properties of light rays in radiative gravitational fields. It presents a theoretical study of the generation, propagation, back-reaction, and detection of gravitational waves from astrophysical sources. After reviewing the various quadrupole-moment laws for gravitational radiation in the Newtonian approximation, we show how to incorporate post-Newtonian corrections into the source multipole moments, the radiative multipole moments at infinity, and the back-reaction potentials. We f…
Polarizations of primordial gravitational waves can be relevant when considering inflationary universe in modified gravity or when matter fields survive during inflation. Such polarizations have been discussed in the Bunch-Davies vacuum. Instead of taking into account dynamical generation of polarizations of gravitational waves, in this paper, we consider polarized initial states constructed from $SU(2)$ coherent states. We then evaluate the power spectrums of the primordial gravitational waves in the states.
The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation.
Any modification on gravity would affect not only gravitational wave (GW) generation but also GW propagation. Therefore, tests of general relativity (GR) with only GW generation or GW propagation will lead to an overestimate for deviations. Here we try to use one set of parameters to parameterize the modifications on both GW generation and GW propagation and then test GR with GW150914. In our simplest case, we find that graviton mass $μ<6.3\times10^{-23}{\rm eV/c^2}$ at $90\%$ C.L. and there are no deviations from GR at $90\%$ C.L..
Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gr…
Circularly polarized gravitational sandwich waves exhibit, as do their linearly polarized counterparts, the Velocity Memory Effect: freely falling test particles in the flat after-zone fly apart along straight lines with constant velocity. In the inside zone their trajectories combine oscillatory and rotational motions in a complicated way. For circularly polarized periodic gravitational waves some trajectories remain bounded, while others spiral outward. These waves admit an additional "screw" isometry beyond the usual five. The consequences of this extra symmetry are explored.
Efforts are underway to improve the design and sensitivity of gravitational waves detectors, with the hope that the next generation of these detectors will observe a gravitational wave signal. Such a signal will not only provide information on dynamics in the strong gravity regime that characterizes potential sources of gravitational waves, but will also serve as a decisive test for alternative theories of gravitation that are consistent with all other current experimental observations. We study the linearized theory of the tensor-vector-scalar theory of gravity (TeVeS) with generalized vector…
Using the Newman-Penrose formalism we calculate the positive energy momentum eigenstates of the Dirac equation for a plane polarized grav- itational wave pulse. We then consider Dirac particles whose spins are polarized in each orthonormal coordinate direction prior to the arrival of the gravitational wave pulse, and determine how the spins are changed by the pulse after its departure.
We examine the recent statement by A. Dolgov and I. Novikov that superluminal propagation of light, which is induced by the quantum corrections to the photon propagation in gravitational field, permits non-causal signal propagation. For this purpose we examine the possibility of the existence of non-causal signals in the model case, when characteristic cone of the signal is outside the usual light cone in Minkowski space-time, as it take place in the case of the photon propagation in gravitation field with quantum corrections taking into account. In such model the signal propagates along invar…
A method is given which renders indirect detection of strong gravitational waves possible. This is based on the reflection (collision) of a linearly polarized electromagnetic shock wave from (with) a cross polarized impulsive and shock gravitational waves in accordance with the general theory of relativity. This highly non-linear process induces a detectable Faraday rotation in the polarization vector of the electromagnetic field.
An exact solution for the expansion of a flat universe with dark energy evolving according to a simple model is explored. The equation for weak primordial gravitational waves propagating in this universe is solved and explored; gravitational waves in a flat cosmology possessing both a "big bang" singularity and a "big rip" singularity can be described with confluent Heun functions. We develop approximation methods for confluent Heun equations in regimes of interest to gravitational wave astronomers and predict the diminution in gravitational wave amplitude in a universe with both a Big Bang an…
Using the Bondi-Sachs formalism, the problem of a gravitational wave source surrounded by a spherical dust shell is considered. Using linearized perturbation theory, the geometry is found in the regions: in the shell, exterior to the shell, and interior to the shell. It is found that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust.
An analytical solution for the light trajectory in the near-zone of the gravitational field of one pointlike body in arbitrary slow-motion in the post-post-Newtonian approximation is presented in harmonic gauge. Expressions for total light deflection and time delay are given. The presented solution is a further step toward high-precision astrometry aiming at nano-arcsecond level of accuracy.
This work establishes a relation between chiral anomalies in curved spacetimes and the radiative content of the gravitational field. In particular, we show that a flux of circularly polarized gravitational waves triggers the spontaneous creation of photons with net circular polarization from the quantum vacuum. Using waveform catalogues we identify precessing binary black holes as astrophysical configurations that emit such gravitational radiation, and then solve the fully non-linear Einstein's equations with numerical relativity to evaluate the net effect. The quantum amplitude for a merger i…
This paper investigates the propagation of polar gravitational waves in the spatially flat FRW universe consisting of a perfect fluid in the scenario of $R+2λT$ model of $f(R,T)$ gravity ($λ$ being the model parameter). The spatially flat universe model is perturbed via Regge-Wheeler perturbations inducing polar gravitational waves and the field equations are formulated for both unperturbed as well as perturbed spacetimes. We solve these field equations simultaneously for the perturbation parameters introduced in the metric, matter, and velocity in the radiation, as well as dark energy, domina…
The "Bargmann framework" allows us to prove the equivalence of the Pais-Uhlenbeck oscillator with a spin-zero particle in a circularly polarized periodic gravitational wave. Pushing forward the symmetries (which include Carroll symmetry) of the latter, we derive conserved charges for the Pais-Uhlenbeck oscillator.
We discuss the propagation of gravitational waves in a recently discussed class of theories containing N >= 2 metric tensors and a corresponding number of standard model copies. Using the formalism of gauge-invariant linear perturbation theory we show that all gravitational waves propagate at the speed of light. We then employ the Newman-Penrose formalism to show that two to six polarizations of gravitational waves may exist, depending on the parameters entering the equations of motion. This corresponds to E(2) representations N_2, N_3, III_5 and II_6. We finally apply our general discussion t…
We present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous method for obtaining gauge-invariant gravitational waveforms from existing and future astrophysical simulations. We demonstrate the new algorithm's stability, convergence, and agreement with existing evolution methods. We explain how an innovative spectral approach enables a two orders of magnitude i…
Disturbing of a spacetime geometry may result in the appearance of an oscillating and damped radiation - the so-called quasinormal modes. Their periods of oscillations and damping coefficients carry unique information about the mass and the angular momentum, that would allow one to identify the source of the gravitational field. In this talk we present recent bounds on the diffused energy, applicable to the Schwarzschild spacetime, that give also rough estimates of the energy of excited quasinormal modes.
In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze here the system of coupled wave equations, deriving combined energy-Morawetz and $r^p$-estimates for the system, in the case of small charge.
We study the interferometric observation of intensity and polarization anisotropies of a stochastic gravitational wave background (SGWB). We show that the observed correlated data is defined in the group manifold of the three-dimensional rotation. Explicit correlation between two detectors in the interferometry experiments such as LIGO-Virgo and KAGRA is constructed in terms of the Wigner D-functions. Our results may provide a tool for constructing data pipelines to estimate the power spectra of the SGWB anisotropies.
Significant gravitational wave emission is expected from gamma-ray bursts arising from compact stellar mergers, and possibly also from bursts associated with fast-rotating massive stellar core collapses. These models have in common a high angular rotation rate, and observations provide evidence for jet collimation of the photon emission, with properties depending on the polar angle, which may also be of relevance for X-ray flashes. Here we consider the gravitational wave emission and its polarization as a function of angle which is expected from such sources. We discuss possible correlations b…
We analyze the propagation of gravitational waves (GWs) in an asymptotically de-Sitter space by expanding the perturbation around Minkowski and introducing the effects of the Cosmological Constant ($Λ$), first as an additional source (de-Donder gauge) and after as a gauge effect ($Λ$-gauge). In both cases the inclusion of the Cosmological Constant $Λ$ impedes the detection of a gravitational wave at a distance larger than $L_{crit}=(6\sqrt{2}πf \hat{h}/\sqrt{5})r_Λ^2$, where $r_Λ=\frac{1}{\sqrtΛ}$ and f and $\hat{h}$ are the frequency and strain of the wave respectively. We demonstrate that $L…
The direct detection of gravitational waves by ground-based interferometers opened an unprecedented channel to probe alternative theories of gravitation. Several theories predict a dispersion of the gravitational waves during their propagation, distorting the signals observed by LIGO and Virgo compared to their predictions from general relativity. Such dispersion could induce a modification of the luminosity distance inferred with gravitational radiation with regards to electromagnetic radiation. By analysing two multimessenger events, we set constraints on a large class of proposed theories, …
In the study of covariant wave equations, linear gravity manifests itself through the metric deviation $γ_{μν}$ and a two-point vector potential $K_λ$ itself constructed from $γ_{μν}$ and its derivatives. The simultaneous presence of the two gravitational potentials is non contradictory. Particles also assume the character of quasiparticles and $K_λ$ carries information about the matter with which it interacts. We consider the influence of $K_λ$ on the dispersion relations of the particles involved, the particles' motion, quantum tunneling through a horizon, radiation, energy-momentum dissipat…
We show that helical turbulence produced during a first-order phase transition generates circularly polarized cosmological gravitational waves (GWs). The characteristic frequency of these GWs for an extreme case of the phase transition model is around $10^{-3}$ --- $10^{-2}$ Hz with an energy density parameter as high as $10^{-12}$ --- $10^{-11}$. The possibility of detection is briefly discussed.
We solve the Laplace equation $\Box h_{ij}=0$ describing the propagation of gravitational waves in an expanding background metric with a power law scale factor in the presence of a point mass in the weak field approximation (Newtonian McVittie background). We use boundary conditions at large distances from the mass corresponding to a standing spherical gravitational wave in an expanding background which is equivalent to a linear combination of an incoming and an outgoing propagating gravitational wave. We compare the solution with the corresponding solution in the absence of the point mass and…
We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave-fronts in the background R…
A GHz maser beam with Gaussian-type distribution passing through a homogenous static magnetic field can be used to detect gravitational waves (GWs) with the same frequency. The presence of GWs will perturb the electromagnetic (EM) fields, giving rise to perturbed photon fluxes (PPFs). After being reflected by a fractal membrane, the perturbed photons suffer little decay and can be measured by a microwave receiver. This idea has been explored to certain extent as a method for very high frequency gravitational waves. In this paper, we examine and develop this method more extensively, and confron…
We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein-Maxwell theory. The post-collision space-times are obtained by solving the vacuum Einstein-Maxwell field equations in the geometrical optics approximation. The head-on collisions of all possible pairs of these systems of waves is described and the results are then generalised to non-linearly polarized waves which exhibit the maximum two degrees of freedom of polarization.
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 ar…
In this second article of the series, we apply our recently derived equation for the electric field propagation along light rays [arXiv:2004.03496], valid on the electromagnetic geometrical optics limit, to the special case of a toy interferometer used to detect gravitational waves in a flat background. Such an equation shows that, assuming the detector is in the transverse-traceless frame, which has a local shearing relative motion due to the gravitational wave perturbations, the electric field does not propagate as in an inertial reference frame in Minkowski spacetime. We present the electri…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized following the prescription in \cite{ncgw1}. Standard algebraic techniques are then employed to solve the Hamiltonian of the system. The solutions, in both cases, show signatures of the coordinate noncommutativity. In the harmonic oscillator case, this signature plays a key role in altering the resonance point and the oscillation frequency of the system.
Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the classical Hamiltonian following \cite{speli}. The rotating polarization vectors of the circularly polarized GW are employed to form a unique directional triad which served as the coordinate axes. The Schrodinger equations for the system are cast in the form of a set of coupled linear differential equations. This system is solved by iterative technique. We compute …
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is anisotropic. Various matter distributions are considered, from the standard dust or radiation distribution to exotic matters like that with an equation of state $P = - \frac{1}{3} ρ$. In almost all cases the frequency and amplitude of the wave are found to be decaying with evolution, except for a closed radiation universe where there is a resurgence of the wavef…
Overlap reduction functions for a polarized stochastic gravitational-wave background in the Einstein Telescope-Cosmic Explorer and the LISA-Taiji networks
本文将基于球谐展开的重叠减少函数计算方法推广到第三代地基 Einstein Telescope-Cosmic Explorer 网络及 LISA-Taiji 空间联合任务，以分析极化随机引力波背景。
We derive a system of equations governing the coupled gravitational and electromagnetic perturbations of Reissner-Nordström spacetime. The equations are derived in the context of global non-linear stability of Reissner-Nordström under axially symmetric polarized perturbations, as a generalization of the recent work on non-linear stability of Schwarzschild spacetime of Klainerman-Szeftel. The main result consists in deriving, through a Chandrasekhar-type transformation, a gauge invariant quantity associated to the electromagnetic tensor that verifies a Regge-Wheeler equation. In this paper, we …
Parity violation is expected to generate an asymmetry between the amplitude of left and right-handed gravitational-wave modes which leads to a circularly polarized stochastic gravitational-wave background (SGWB). Due to the three independent baselines in the LIGO-Virgo network, we focus on the amplitude difference in strain power characterized by Stokes' parameters and do maximum-likelihood estimation to constrain the polarization degree of SGWB. Our results indicate that there is no evidence for the circularly polarized SGWB in the data. Furthermore, by modeling the SGWB as a power-law spectr…
Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method in the gravitational field of an isolated, gravitationally bound N-body system. Different from the traditional $N$ bodies that are independent with each other in the system, our system includes the velocities, accelerations, gravitational interactions and tidal deformations of the gravitational bodies. The light delays of these factors then are precisely dete…
We show how to derive the equations of light propagation in the gravitational field of uniformly moving mass monopoles without formulating and integrating the differential equations of light propagation in that field. The well-known equations of light propagation in the gravitational field of a motionless mass monopole are combined with a suitable Lorentz transformation. The possibility to generalize this technique for the more complicated case of uniformly moving body of arbitrary multipole structure is discussed.
The propagation of gravitational waves is explored in the cosmological context. It is explicitly demonstrated that the propagation of gravitational waves could be influenced by the medium. It is shown that in the thermal radiation, the propagation of gravitational waves in general relativity is different from that in the scalar-tensor theory. The propagation of gravitational waves is investigated in the uniform magnetic field. As a result, it is found that cosmic magnetic fields could influence on the propagation of gravitational waves to non-negligible extent. The corresponding estimation for…
