Gravitational Faraday Effect Research Articles

Faraday effect of light caused by plane gravitational wave

A gravitational field can cause a rotation of the polarisation vector of light. This phenomenon is known as the gravitational Faraday effect. We study the gravitational Faraday effect of linearly polarised light propagating in the gravitational field of a weak plane gravitational wave (GW) with “+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$+$$\\end{document}", “×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document}", and elliptical polarisation modes. The corresponding gravitational Faraday rotation angle is proportional to the GW amplitude and to the squared distance traveled by the light and inversely proportional to the GW squared wavelength. The Faraday rotation is maximal if the light propagates along directions perpendicular to the GW propagation and tilted by π/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi /4$$\\end{document} to the directions of its polarisation. There is no a gravitational Faraday rotation when light and a GW propagate along the same directions, or when light propagates along directions of a GW polarisation. Helicity of an elliptically polarised GW gives cubic order contribution to the Faraday rotation.

Gravitational Faraday effect from on-shell amplitudes

Effects of massive object’s spin on massive-massless 2 → 2 classical scattering is studied. Focus is set on the less-considered dimensionless expansion parameter λ/b, where λ is the massless particle’s wavelength and b is the impact parameter. Corrections in λ/b start to appear from mathcal{O} (G2), with leading correction terms tied to the gravitational Faraday effect, which is a special case of the Lense-Thirring effect. We compute the eikonal phase up to mathcal{O} (G2) and extract spin effect on the scattering angle and time delay up to 14th order in spin. The gravitational Faraday effect at linear order in spin [1] is reproduced by λ/b correction terms, which we compute to higher orders in spin. We find that the equivalence principle, or universality, holds up to NLO for general spinning bodies, i.e. away from geometric optics limit. Furthermore, in the black hole limit, we confirm the absence of particular spin structure observed [2–8], along with the associated shift symmetry [7], and argue that it holds to arbitrary spin order at mathcal{O} (G2) in the massless probe limit.

Gravitational analog of Faraday rotation in the magnetized Kerr and Reissner-Nordström spacetimes

It is known that the gravitational analog of the Faraday rotation arises in the rotating spacetime due to the nonzero gravitomagnetic field. In this paper, we show that it also arises in the "nonrotating" Reissner-Nordstr\"om spacetime, if it is immersed in a uniform magnetic field. The non-zero angular momentum (due to the presence of electric charge and magnetic field) of the electromagnetic field acts as the twist potential to raise the gravitational Faraday rotation as well as the gravitational Stern-Gerlach effect in the said spacetimes. The twisting can still exist even if the mass of the spacetime vanishes. In other words, the massless charged particle(s) immersed in a uniform magnetic field are able to twist the spacetime in principle, and responsible for the rotation of the plane of polarization of light. This, in fact, could have applications in the basic physics and the analog models of gravity. Here, we also study the effect of magnetic fields in the Kerr and Reissner-Nordstr\"om spacetimes, and we derive the exact expressions for the gravitational Faraday rotation and the gravitational Stern-Gerlach effect in the magnetized Kerr and Reissner-Nordstr\"om spacetimes. Calculating the lowest order of the gravitational Faraday effect arisen due to the presence of a magnetic field, we show that the logarithm correction of the distance of the source and observer in the gravitational Faraday rotation and gravitational Stern-Gerlach effect for the said spacetimes is an important consequence of the presence of the magnetic field. From the astrophysical point of view, our result could be helpful to study the effects of (gravito)magnetic fields on the propagation of polarized photons in the strong gravity regime of the collapsed object.

Polarization rotation and near-Earth quantum communications

We revisit polarization rotation due to gravity, known as the gravitational Faraday effect, with a view on its role in quantum communications with Earth-orbiting satellites. In a static spherically symmetric gravitational field Faraday rotation is purely a reference frame (gauge) effect. This is so also in the leading post-Newtonian expansion of the Earth's gravitational field. However, establishing the local reference frame with respect to distant stars leads to the nonzero Faraday phase. In communications between a ground station and an Earth-orbiting spacecraft this phase is of the order of 10^-10. Under the same conditions the Wigner phase of special relativity is typically of the order 10^-4--10^-5. These phases lead to the physical lower bound on communication errors. However, both types of errors can be simultaneously mitigated. Moreover, they are countered by a fully reference frame independent scheme that also handles arbitrary misalignment between the reference frames of sender and receiver.

Gravitational Faraday and spin-Hall effects of light

The gravitational Faraday and its dual spin-Hall effects of light arise in space-times of non-zero angular momentum. These effects were studied in stationary, asymptotically flat space-times. Here we study these effects in arbitrary, non-stationary, asymptotically flat space-times. These effects arise due to interaction between light polarisation and space-time angular momentum. As a result of such interaction, the phase velocity of left- and right-handed circularly polarised light becomes different, that results in the gravitational Faraday effect. This difference implies different dynamics of these components, that begin to propagate along different paths\textemdash the gravitational spin-Hall effect of light. Due to this effect, the gravitational field splits a multicomponent beam of unpolarized light and produces polarized gravitational rainbow. The component separation is an accumulative effect observed in long range asymptotics. To study this effect, we construct uniform eikonal expansion and derive dynamical equation describing this effect. To analyse the dynamical equation, we present it in the local space and time decomposition form. The spatial part of the equation presented in the related optical metric is analogous to the dynamical equation of a charged particle moving in magnetic field under influence of the Coriolis force.

Rotation of polarization in the gravitational field of a laser beam—Faraday effect and optical activity

We investigate the rotation of the polarization of a light ray propagating in the gravitational field of a circularly polarized laser beam. The rotation consists of a reciprocal part due to gravitational optical activity, and a non-reciprocal part due to the gravitational Faraday effect. We discuss how to distinguish the two effects: letting light propagate back and forth between two mirrors, the rotation due to gravitational optical activity cancels while the rotation due to the gravitational Faraday effect accumulates. In contrast, the rotation due to both effects accumulates in a ring cavity and a situation can be created in which gravitational optical activity dominates. Such setups amplify the effects by up to five orders of magnitude, which however is not enough to make them measurable with state of the art technology. The effects are of conceptual interest as they reveal gravitational spin–spin coupling in the realm of classical general relativity, a phenomenon which occurs in perturbative quantum gravity.

ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION

Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar X-ray emission region to be of the order of 10 gravitational radii of the central supermassive black hole. For distances within a few gravitational radii, light paths are strongly bent by the strong gravity field of the central black hole. If the central black hole has nonzero angular momentum (spin), a photon's polarization plane will be rotated by the gravitational Faraday effect. The observed X-ray flux and polarization will then be influenced significantly by the strong gravity field near the source. Consequently, linear gravitational lensing theory is inadequate for such extreme circumstances. We present simple algorithms computing strong lensing effects of Kerr black holes, including effects on polarization. Our algorithms are realized in a program "KERTAP" in two versions: MATLAB and Python. The key ingredients of KERTAP are: a graphic user interface, a {\it backward} ray-tracing algorithm, a polarization propagator dealing with gravitational Faraday rotation, and algorithms computing observables such as flux magnification and polarization angles. Our algorithms can be easily realized in other programming languages such as FORTRAN, C, and C++. The MATLAB version of KERTAP is parallelized using the MATLAB Parallel Computing Toolbox and the Distributed Computing Server. The Python code was sped up using Cython and supports full implementation of MPI using 'mpi4py' package. As an example, we investigate the inclination angle dependence of the observed polarization and the strong lensing magnification of AGN X-ray emission. We conclude that it is possible to perform complex numerical-relativity-related computations using interpreted languages such as MATLAB and Python.

Gravitational Faraday Effect Produced by a Ring Laser

Using the linearized Einstein gravitational field equations and the Maxwell field equations it is shown that the plane of polarization of an electromagnetic wave is rotated by the gravitational field created by the electromagnetic radiation of a ring laser. It is further shown that this gravitational Faraday effect shares many of the properties of the standard electromagnetic Faraday effect. An experimental arrangement is then suggested for the observation of this gravitational Faraday effect induced by the ring laser.

Gravitational faraday effect in curved space-time induced by high-power lasers

Gravitational field produced by high-power laser is calculated according to the linearized Einstein field equation in weak field approximation. Gravitational Faraday effect of electromagnetic wave propagating in the above gravitational field is studied and the rotation angle of polarization plane of electromagnetic wave is derived. The result is discussed and estimated under the condition of present experiment facility.

Gravitational effects induced by high-power lasers

The gravitational field produced by a high-power laser is calculated according to the linearized Einstein field equation in weak field approximation. It is found that when a probe pulse propagates in the above gravitational field, the gravitational Faraday effect and defocusing phenomenon of the probe pulse are induced by the gradient of the energy density of the high-power laser pulse. The rotating angle of the polarization plane of the probe pulse and the variation of its light intensity are derived. The results are discussed and estimated under the conditions of our present experiment facility.

Can the rotation of the dark matter halo of our galaxy be detected through its effect on thecosmic microwave background polarization?

The proposition that dark matter halos possess angular momentum, though widelyaccepted, is a theoretical prediction which has, to date, not been observationally verified.The gravomagnetic field produced by a rotating gravitating object is possibly the onlydirect consequence of the angular momentum of dark matter halos. The gravitationalFaraday rotation produced by the dark matter halo of our galaxy is present inall astronomical observations. A detection of the imprint of this effect on theall-sky cosmic microwave background radiation polarization pattern would directlyprobe the angular momentum of the dark matter halo of our galaxy. We havecalculated the expected gravitational Faraday rotation which turns out to be a(vc/c)3 effect,vc beingthe rotational speed of our halo. The predicted gravitational Faraday effect rotation angles are much lessthan 1′′, implying that this effect, though present, is too small to be detected.

GRAVITATIONAL FARADAY EFFECT INDUCED BY HIGH-POWER LASERS

Gravitational field produced by high-power laser is calculated according to the linearized Einstein field equation in weak field approximation. Gravitational Faraday effect of electromagnetic wave propagating in the above gravitational field is studied and the rotation angle of polarization plane of electromagnetic wave is derived. The result is discussed and estimated in the condition of present experimental facility.

Effect of the Quadrupole Moment of a Rotating MassiveObject on the Gravitational Faraday Rotation

We study the rotation of the polarization plane for a ray ofelectromagnetic radiation propagating in the gravitoelectromagneticfield caused by a rotating massive object with the quadrupole moment.The effect of the quadrupole moment on the gravitational Faradayrotation is investigated. It is found that the gravitational Faradayeffect of the quadrupole moment is negligible for Kerr black holes, butthis effect is important for rapidly rotating neutron stars.

Gravitational Faraday effect in conformally stationary spacetimes

For conformally stationary spacetimes it is possible to formulate the geometric optics approximation of light propagation purely in terms of the geometry of the three-dimensional manifold M consisting of the integral curves of the conformal Killing vector field. In this framework they derive the transport law for the polarization plane in M. If the conformal Killing field has a non-vanishing twist, the polarization plane undergoes a rotation similar to the familiar Faraday rotation in a magnetic field. This so-called gravitational Faraday effect is of particular interest in the gravitational field of rotating matter where is is coupled to the angular momentum of this matter. Therefore, they illustrate their general results with three rotating matter examples, namely (i) an Ozsvath-Schucking spacetime; (ii) the gravitational field outside a rotating body and (iii) a Kerr black hole embedded into a Robertson-Walker cosmos. Thereby they roughly estimate the observability of the gravitational Faraday effect in solar system experiments and in connection with the gravitational lens effect.