We provide analysis to determine the effects of gravitational waves on electromagnetic waves, using perturbation theory in general relativity. Our analysis is performed in a completely covariant manner without invoking any coordinates. For a given observer, in the geometrical-optics approximation, we work out the perturbations of the phase, amplitude, frequency and polarization properties--axes of ellipse and ellipticity of light, due to gravitational waves. With regard to the observation of gravitational waves, we discuss the measurement of Stokes parameters, through which the antenna patterns are presented to show the detectability of the gravitational wave signals.
The polarization of electromagnetic waves in the presence of a gravitational wave is analyzed. The rotation of the polarization angle and the Stokes parameters are deduced. A possible application to the detection of stochastic background of gravitational waves is proposed as a complement to the pulsar timing method.
We find polarization modes of gravitational waves in topologically massive and new massive gravities by using the Newman-Penrose formalism where the null real tetrad is necessary to specify gravitational waves. The number of polarization modes is two for the new massive gravity and one for the topologically massive gravity, which is consistent with the metric-perturbation approach.
Gravitational waves have only two polarization modes in General Relativity. However, there are six possible modes of polarization in metric theory of gravity in general. The tests of gravitational waves polarization can be tools for pursuing the nature of space-time structure. The observations of gravitational waves with a world-wide network of interferometric detectors such as Advanced LIGO, Advanced Virgo and KAGRA will make it possible to obtain the information of gravitational wave polarization from detector signals. We study the separability of the polarization modes for the inspiral grav…
To determine the polarization character of gravitational waves, we use strain data from the GW170814 binary black hole coalescence event detected by the three LIGO-Virgo observatories, extracting the gravitational wave strain signal amplitude ratios directly from those data. Employing a geometric approach that links those ratios to the gravitational wave polarization properties, we find that there is a range of source sky locations, partially overlapping the LIGI-Virgo 90% credible range of GW170814 source locations, for which vector polarization is consistent with the observed amplitude ratio…
A model for the static weak-field macroscopic medium is analyzed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of Newtonian gravity. In case of the strong gravitational quadrupole polarization it essentially holds inside a macroscopic matter source. Outside the source the gravitational potential fades away exponentially. The equation is equivalent to a system of the Poisson equation and the nonhomogeneous modified Helmholtz equations. The general solution to this system is obt…
Similar to the light, gravitational waves traveling in multiple paths may arrive at the same location if there is a gravitational lens on their way. Apart from the magnification of the amplitudes and the time delay between the gravitational wave rays, gravitational lensing also rotates their polarization planes. This results in the changes in the antenna pattern function, which describes the response of the detector to its relative orientation to the gravitational wave. These effects are all reflected in the strain, the signal registered by the interferometers. The gravitational wave rays in v…
Vacuum gravitational fields invariant for a non Abelian Lie algebra generated by two Killing fields whose commutator is light-like are analyzed. It is shown that they represent nonlinear gravitational waves obeying to two nonlinear superposition laws. The energy and the polarization of this family of waves are explicitely evaluated.
We present a new measure for the comparison of unknown gravitational wave signals in two detectors, without recurring to an {\it a priori} template. We apply this measure to the LIGO data of the GW150914 event and discover that Hanford and Livingston observatories have recorded two different components of the gravitational wave polarization signal.
In this technical note, we study the possibility of using networks of ground-based detectors to directly measure gravitational-wave polarizations using signals from compact binary coalescences. We present a simple data analysis method to partially achieve this, assuming presence of a strong signal well-captured by a GR template.
The second post-Newtonian (2PN) contribution to the `plus' and `cross' gravitational wave polarizations associated with gravitational radiation from non-spinning, compact binaries moving in elliptic orbits is computed. The computation starts from our earlier results on 2PN generation, crucially employs the 2PN accurate generalized quasi-Keplerian parametrization of elliptic orbits by Damour, Schäfer and Wex and provides 2PN accurate expressions modulo the tail terms for gravitational wave polarizations incorporating effects of eccentricity and periastron precession.
We analyze the propagation of gravitational waves in a molecular matter medium: our findings demonstrate that dispersion only is expected, together with the emergence of three extra polarizations, able to induce longitudinal stresses. We also give quantitative estimates of the predicted effects.
Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. These forms are related by a coordinate transformation, so they should describe essentially the same physics, but the two forms treat polarization states quite differently. Both deal well with linear polarizations, but there is a qualitative difference in the way they deal with circular, elliptic, and more general polarization states. In this article we will describe a general algorithm for constructing arbitrary polarization states in the Rosen form.
In this paper, we study the gravitational wave polarization modes for some particular $f(R)$ models using Newman-Penrose formalism. We find two extra scalar modes of gravitational wave (longitudinal and transversal modes) in addition to two tensor modes of general relativity. We conclude that gravitational waves correspond to class $II_{6}$ under the Lorentz-invariant E(2) classification of plane null waves for these $f(R)$ models.
The question of the correspondence between the number of degrees of freedom and the number of polarization states in hybrid metric-Palatini f(R)-gravity is considered. It is shown that the scalar transverse breathing and longitudinal modes are a mixture of one polarization state. The speed of gravitational waves propagation in hybrid f(R)-gravity is calculated.
Two polarization modes of gravitational wave are derived from the general relativity which are plus and cross modes. However, the alternative theories of gravity can yield the gravitational wave with up to six polarizations. Searching for the polarizations beyond plus and cross is an important test of general relativity. In principle, one space-borne detector, like LISA, could measure the gravitational wave polarizations from a long time observation with its orbital motion. With the comparable sensitivities, the joint LISA and TAIJI missions will improve the observations on the polarization pr…
We compute analytically the tidal field and polarizations of an exact gravitational wave generated by a cylindrical beam of null matter of finite width and length in quadratic curvature gravity. We propose that this wave can represent the gravitational wave that keep up with the high energy photons produced in a gamma ray burst (GRB) source.
The formalism of the exact six polarization modes of gravitational waves is constructed in terms of both the small metric perturbations and the Newman-Penrose scalars. The obtained formulae are applicable to any metric-compatible gravity theories whose gravitational waves propagate along either the null or non-null geodesics. Once a gravity theory, specifically its linearized wave equation, is written, comparison to the observed data of the laser interferometer experiments is direct.
We determine the possible gravitational wave polarizations in two general classes of teleparallel gravity theories, using the metric and symmetric teleparallel geometries. For this purpose we apply the Newman-Penrose formalism, and find that depending on the choice of parameters, the $\mathrm{E}(2)$ class of the theories is one of $\mathrm{N}_2, \mathrm{N}_3, \mathrm{III}_5, \mathrm{II}_6$, corresponding to two to six polarizations, where all of them include the two tensor polarizations known from general relativity. We also find classes of theories apart from general relativity which yield th…
Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. While these two metric ansatze are related by a coordinate transformation, so that they should describe essentially the same physics, they rather puzzlingly seem to treat polarization states quite differently. Both ansatze deal equally well with + and X linear polarizations, but there is a qualitative difference in they way they deal with circular, elliptic, and more general polarization states. In this article we will develop a general formalism for dealing with arbitrary polarization states i…
The Gaia mission offers a new opportunity to search for the low frequency gravitational wave background using astrometric measurements. In this paper, the astrometric effect of gravitational waves is reviewed, with a particular focus on the effect of non-Einsteinian gravitational wave polarizations. A stochastic gravitational wave background generates a correlated vector field of astrometric deflections on the sky. A convenient decomposition for the correlation matrix is introduced, enabling it to be calculated for all possible gravitational wave polarizations and compared to the redshift corr…
The interaction between gravitational and electromagnetic waves in the presence of a static magnetic field is studied. The field strength of the static field is allowed to surpass the Schwinger critical field, such that the quantum electrodynamical (QED) effects of vacuum polarization and magnetization are significant. Equations governing the interaction are derived and analyzed. It turns out that the energy conversion from gravitational to electromagnetic waves can be significantly altered due to the QED effects. The consequences of our results are discussed.
In this paper, we investigate the sensitivity to additional gravitational wave polarization modes of future detectors. We first look at the upcoming Einstein Telescope and its combination with existing or planned Earth-based detectors in the case of a stochastic gravitational wave background. We then study its correlation with a possible future space-borne detector sensitive to high-frequencies, like DECIGO. Finally, we adapt those results for a single GW source and establish the sensitivity of the modes, as well as the localization on the sky.
The direct detection of gravitational waves by LIGO/Virgo opened the possibility to test General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyzed the polarizations contents of Horndeski theory and $f(R)$ gravity. We found out that in addition to the familiar plus and cross polarizations, a \emph{massless} Horndeski theory predicts an extra trans…
In our previous work \cite{PTA2} we calculated the overlap reduction function for the tensor polarization without employing the short wavelength approximation, this was done by obtaining a power series of nested sums which is valid for all gravitational wave frequencies and pulsar distances. In this work we generalize the power-series expansion method to vector and scalar polarizations. We have compared our expression for the breathing and vector modes with previous literature. We present for the first time analytic expressions for the overlap reduction function of the longitudinal mode for al…
In general relativity, a gravitational wave has two polarization modes (tensor mode), but it could have additional polarizations (scalar and vector modes) in the early stage of the universe, where the general relativity may not strictly hold and/or the effect of higher-dimensional gravity may become significant. In this paper, we discuss how to detect extra-polarization modes of stochastic gravitational wave background (GWB), and study the separability of each polarization using future space-based detectors such as BBO and DECIGO. We specifically consider two plausible setups of the spacecraft…
The polarization vector (PV) of an electromagnetic wave (EW) will experience a rotation in a region of spacetime perturbed by gravitational waves (GWs). Based on this idea, Cruise's group has built an annular waveguide to detect GWs. We give detailed calculations of the rotations of the polarization vector of an EW caused by incident GWs from various directions and in various polarization states, and then analyze the accumulative effects on the polarization vector when the EW passes n cycles along the annular waveguide. We reexamine the feasibility and limitation of this method to detect GWs o…
We investigate the detectability of massive mode of polarization of Gravitational Waves (GWs) in f(R) theory of gravity associated with Gamma Ray Bursts (GRBs) sources. We obtain the beam pattern function of Laser Interferometric Gravitational wave Observatory (LIGO) corresponding to the massive polarization of GWs and perform Bayesian analysis to study this polarization. It is found that the massive polarization component with a mass of 10^-22eV/c2 is too weak to be detected at LIGO with its current configuration.
The recently proposed Skordis-Złośnik theory is the first relativistic MOND theory that can recover the success of the standard $Λ$CDM model at matching observations of the cosmic microwave background. This paper aims to revisit the Newtonian and MOND approximations and the gravitational wave analysis of the theory. For the local gravitational parameters, we show that one could obtain both time-varying effective Newtonian gravitational \textit{constant} $G_\textrm{N}$ and time-varying characteristic MOND acceleration scale $a_\textrm{MOND}$, by relaxing the static assumption extensively adopte…
The influence of the weak gravitational wave on the light polarization is considered. Oscillations in the direction of the polarization vector is found.
An additional scalar degree of freedom for a gravitational wave is often predicted in theories of gravity beyond general relativity and can be used for a model-agnostic test of gravity. In this letter, we report the direct search for the scalar-tensor mixed polarization modes of gravitational waves from compact binaries in a strong regime of gravity by analyzing the data of GW170814 and GW170817, which are the merger events of binary black holes and binary neutron stars, respectively. Consequently, we obtain the constraints on the ratio of scalar-mode amplitude to tensor-mode amplitude: $\less…
The direct detection of gravitational waves provides the opportunity to measure fundamental aspects of gravity which have never been directly probed before, including the polarization of gravitational waves. In the context of searches for continuous waves from known pulsars, we present novel methods to detect signals of any polarization content, measure the modes present and place upper-limits on the amplitude of non-tensorial components. This will allow us to obtain new model-independent, dynamical constraints on deviations from general relativity. We test this framework on multiple potential…
The relative acceleration between two nearby particles moving along accelerated trajectories is studied, which generalizes the geodesic deviation equation. The polarization content of the gravitational wave in Horndeski theory is investigated by examining the relative acceleration between two self-gravitating particles. It is found out that the longitudinal polarization exists no matter whether the scalar field is massive or not. It would be still very difficult to detect the enhanced longitudinal polarization with the interferometer, as the violation of the strong equivalence principle of mir…
In a general metric theory of gravitation in four dimensions, six polarizations of a gravitational wave are allowed: two scalar and two vector modes, in addition to two tensor modes in general relativity. Such additional polarization modes appear due to additional degrees of freedom in modified gravity theories. Also graviton mass, which could be different in each polarization, is another characteristic of modification of gravity. Thus, testing the existence of additional polarization modes and graviton mass can be a model-independent test of gravity theories. Here we extend the previous frame…
The detection of the first gravitational wave events by the Advanced LIGO Scientific Collaboration has opened a new possibility for the study of fundamental physics of gravitational interaction. This work conducts an analysis of possible polarization states of gravitational waves (GW) radiated by the most promising types of sources to be detected by the modern interferometric antennas: coalescing compact binaries and collapsing supernovae. Several theoretical approaches to the current as well as future gravitational wave signals interpretation are discussed together with a strategy for a searc…
The detection of gravitational wave (GW) has opened a new window to test the theory of gravity in the strong field regime. In general relativity (GR), GW can only possess two tensor polarization modes, which are known as the $+$ and $\times$ modes. However, vector and scalar modes can exist in some modified theories of gravity, and we can test the gravitational theories by probing these extra polarization modes. As a space-borne GW detector, TianQin will be launched in the 2030s, and it is expected to observe plenty of GW signals, including those from nearly ten-thousands double white dwarfs (…
We study the detectability of circular polarization in a stochastic gravitational wave background from various sources such as supermassive black hole binaries, cosmic strings, and inflation in the early universe with pulsar timing arrays. We calculate generalized overlap reduction functions for the circularly polarized stochastic gravitational wave background. We find that the circular polarization can not be detected for an isotropic background. However, there is a chance to observe the circular polarization for an anisotropic gravitational wave background. We also show how to separate polar…
There are conflicting statements in the literature about the gravitational Faraday rotation of the plane of polarization of polarized electromagnetic radiation travelling through a gravitational wave. This issue is reconsidered using a simple formalism describing the rotation of the plane of polarization in a gravitational field, in the geometric optics approximation. It is shown that, to first order in the gravitational wave amplitude, the rotation angle is a boundary effect which vanishes for localized (astrophysically generated) gravitational waves and is non-zero, but nevertheless negligib…
General Relativity predicts only two tensor polarization modes for gravitational waves while at most six possible polarization modes are allowed in general metric theory of gravity. The number of polarization modes is determined by the specific modified theory of gravity. Therefore, the determination of polarization modes can be used to test gravitational theory. We introduce a concrete data analysis pipeline for a space-based detector such as LISA to detect the polarization modes of gravitational waves. This method can be used for monochromatic gravitational waves emitted from any compact bin…
In a recent paper "Probing gravitational wave polarizations with signals from compact binary coalescences" (arXiv:1710.03794 [gr-qc]) the authors argue that a single detection of gravitational wave by the LIGO-Virgo network is capable to distinguish between pure tensor and pure vector polarizations of gravitational waves. Here we point out a mistake in the author's analysis and show that such differentiation is possible only in the unlikely event when gravitational wave propagates in the direction of interferometer zero response for the tensor or vector polarizations. Nevertheless, the LIGO-Vi…
After a brief review of the work of de Paula, Miranda and Marinho on massive gravitational waves arising from a bimetric theory of gravity, in this paper it is shown that the presence of the mass generates a longi- tudinal component in a particular polarization of the wave. The effect of this polarization on test masses is performed using the geodesic deviation. A the end of this paper the detectability of this particular polarization is also discussed, showing that its angular dependence could, in princi- ple, discriminate such polarization with respect the two ones of general relativity, if …
In a general metric theory of gravitation in four dimensions, six polarizations of a gravitational wave are allowed: two scalar and two vector modes, in addition to two tensor modes in general relativity. Such additional polarization modes appear due to additional degrees of freedom in modified theories of gravitation or theories with extra dimensions. Thus, observations of gravitational waves can be utilized to constrain the extended models of gravitation. In this paper, we investigate detectability of additional polarization modes of gravitational waves, particularly focusing on a stochastic…
Alternative LISA-TAIJI networks: polarization separation of the stochastic gravitational wave background
Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术研究院）；Department of Physics, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院）；Department of Physics, Faculty of Arts and Sciences, Beijing Normal University（北京师范大学艺术与科学学院物理系）
There exist six possible polarization modes of gravitational waves in general metric theory of gravity, while two tensor polarization modes are allowed in general relativity. The properties and number of polarization modes depend on gravity theories. The number of the detectors needs to be equal to the number of the polarization modes of the gravitational waves for separation of polarizations basically. However, a single detector having great sensitivity at lower frequency could be effectively regarded as a virtual detector network including a set of detectors along its trajectory due to a lon…
We derive a relation between the two polarization modes of a plane, linear gravitational wave in the second-order approximation. Since these two polarizations are not independent, an initially monochromatic gravitational wave loses its periodic character due to the nonlinearity of the Einstein field equations. Accordingly, real gravitational waves may differ from solutions of the linearized field equations, which are being assumed in gravitational-wave detectors.
In this paper, we study the properties of gravitational waves in the scalar-tensor-vector gravity theory. The polarizations of the gravitational waves are investigated by analyzing the relative motion of the test particles. It is found that the interaction between the matter and vector field in the theory leads to two additional transverse polarization modes. By making use of the polarization content, the stress-energy pseudo-tensor is calculated by employing the perturbed equation method. Besides, the relaxed field equation for the modified gravity in question is derived by using the Landau-L…
Alternative theories of gravity predict up to six distinct polarization modes for gravitational waves. Strong gravitational lensing of gravitational waves allows us to probe the polarization content of these signals by effectively increasing the number of observations from the same astrophysical source. The lensing time delays due to the multiple observed lensed images combined with the rotation of the Earth allows for effective non-collocated interferometers to be defined with respect to the source location and hence probe the alternative polarization amplitudes with more observations. To mea…
Recent breakthroughs in numerical relativity enable one to examine the validity of the post-Newtonian expansion in the late stages of inspiral. For the comparison between post-Newtonian (PN) expansion and numerical simulations, the waveforms in terms of the spin-weighted spherical harmonics are more useful than the plus and cross polarizations, which are used for data analysis of gravitational waves. Factorized resummed waveforms achieve better agreement with numerical results than the conventional Taylor expanded post-Newtonian waveforms. In this paper, we revisit the post-Newtonian expansion…
Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in $f(R)$ theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show tha…
We discuss the contribution of gravitational wave to the cosmic microwave background radiation (CMBR) anisotropy and polarization. It is found that the large-scale polarization of CMBR is less than 1\% for a standard recombination universe. The effect of matter reionization will enhance the CMBR polarization to a 10\% level. We have computed the CMBR polarization for two extreme cases (not absolutely ruled out) and found that further enhancement of the ratio is possible. We conclude that measuring the polarization of CMBR on large-angular scales can probe the ionization history of the early un…
The canonical quantization of the essentially nonlinear midisuperspace model describing cylindrically symmetric gravitational waves with two polarizations is presented. A Fock space type representation is constructed. It is based on a complete set of quantum observables. Physical expectation values may be calculated in arbitrary excitations of the vacuum. Our approach provides a non-linear generalization of the quantization of the collinearly polarized Einstein-Rosen gravitational waves.
