Linear and rotational dragging effects of gravitational waves on local inertial frames are studied in purely vacuum spacetimes. First the linear dragging caused by a simple cylindrical pulse is investigated. Surprisingly strong transversal effects of the pulse are exhibited. The angular momentum in cylindrically symmetric spacetimes is then defined and confronted with some results in literature. In the main part, the general procedure is developed for studying weak gravitational waves with translational but not axial symmetry which can carry angular momentum. After a suitable averaging the rotation of local inertial frames due to such rotating waves can be calculated explicitly and illustrated graphically. This is done in detail in the accompanying paper. Finally, the rotational dragging is given for strong cylindrical waves interacting with a rotating cosmic string with a small angular momentum.
There is a drag force on objects moving in the background cosmological metric, known from galaxy cluster dynamics. The force is quite small over laboratory timescales, yet it applies in principle to all moving bodies in the universe. It means it is possible for matter to exchange momentum and energy with the gravitational field of the universe, and that the cosmological metric can be determined in principle from local measurements on moving bodies. The drag force can be understood as inductive rectilinear frame dragging. This dragging force exists in the rest frame of a moving object, and aris…
In this paper, we review and analyze four specific general-relativistic problems in which gravitomagnetism plays an important role: the dragging of magnetic fields around rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, compared with the dragging by rotating gravitational waves. We demonstrate how the quantum detection of inertial frame dragging can be accomplished by using the Unruh-DeWitt detectors. Finally, we shall briefly show how ``instantaneous Machian gauges'' can be useful in the cosmological perturbation theory.
Frame-dragging effect manifests itself as polarization direction rotation when linearly polarized electromagnetic/gravitational wave scatters from a spinning point source through gravitational interactions, an effect also known as the gravitational Faraday rotation. Treating general relativity as an effective field theory, the Faraday rotation angle and its quantum corrections are computed using scattering amplitudes. While the classical rotation angle is universal as expected from the equivalence principle, the quantum corrections are found to be different between electromagnetic and gravitat…
We investigate the Hong-Ou-Mandel (HOM) effect $-$ a two-photon quantum-interference effect $-$ in the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding general-relativis…
While the geodesic motion around a Kerr black hole is fully integrable and therefore regular, numerical explorations of the phase-space around other spacetime configurations, with a different multipolar structure, have displayed chaotic features. In most of these solutions, the role of the purely general relativistic effect of frame-dragging in chaos has eluded a definite answer. In this work, we show that, when considering neutral test particles around a family of stationary axially-symmetric analytical exact solution to the Einstein-Maxwell field equations, frame-dragging (as captured throug…
Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magnetic field deforms the star, making it axisymmetric with respect to the magnetic axis (the body symmetry axis). In magnetars, the rotation axis is tilted to the magnetic axis, and we have an oblique rotator. General relativistic treatment of the obliquely rotating magnetar gives rise to frame-dragging velocities both in the azimuthal and polar direction. Solving the Einstein equation up to first-order perturbation in rotation and second-order perturbation in the magnetic field, we calculate the geodes…
I impose the Newtonian criteria of inertial frames on the c.o.m. trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schrödinger equation eliminates the Brownian motion of the c.o.m., restores the exact inertial motion for free masses. For the collapse of Schrödinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m. ---inevitable in the collap…
We investigate the redshift and blueshift of light emitted by timelike geodesic particles in orbits around a Kerr-Newman-(anti) de Sitter (KN(a)dS) black hole. Specifically we compute the redshift and blueshift of photons that are emitted by geodesic massive particles and travel along null geodesics towards a distant observer-located at a finite distance from the KN(a)dS black hole. For this purpose we use the Killing-vector formalism and the associated first integrals-constants of motion. We consider in detail stable timelike equatorial circular orbits of stars and express their corresponding…
Timing a pulsar in a close orbit around the supermassive black hole SgrA* at the center of the Milky Way would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity and alternative modified gravity theories. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravitational field of the black hole. Due to the extreme mass ratio of the pulsar and the supermassive back hole we use the test particle limit to derive an exact analytical formula for the propag…
We study the absorption of plane waves by Kerr black holes. We calculate the absorption cross section: the area of the black hole shadow at a finite wavelength. We present a unified picture of the absorption of all massless bosonic fields, focussing on the on-axis incidence case. We investigate the spin-helicity effect, arising from a coupling between dragging of frames and the helicity of a polarized wave. We introduce and calibrate an extended sinc approximation which provides new quantitative data on the spin-helicity effect in strong-field gravity.
In a geocentric kinematically rotating ecliptical coordinate system in geodesic motion through the deformed spacetime of the Sun, both the longitude of the ascending node $Ω$ and the inclination $I$ of an artificial satellite of the spinning Earth are affected by the post-Newtonian gravitoelectric De Sitter and gravitomagnetic Lense-Thirring effects. By choosing a circular orbit with $I = Ω= 90°$ for a potential new spacecraft, which we propose to name ELXIS, it would be possible to measure each of the gravitomagnetic precessions separately at a percent level, or, perhaps, even better dependin…
Kochi University（高知大学）；Indian Institute of Science（印度科学学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；University of Tübingen（蒂宾根大学）
We compute the equation of state for an ensemble of degenerate fermions by using the curved spacetime of a slowly rotating axially symmetric star. We show that the equation of state computed in such curved spacetime depends on the gravitational time dilation as well as on the dragging of inertial frames, unlike an equation of state computed in a globally flat spacetime. The effect of gravitational time dilation leads to a significant enhancement of the maximum mass limit of a degenerate neutron star. However, such an enhancement due to the frame-dragging effect is extremely small. Nevertheless…
Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by rotating massive objects, which is one of the important, yet studied characteristics of lensed gravitational waves (GWs). In this work, we calculate the GFR angle $χ_g$ of GWs in the weak deflection limit, assuming it is lensed by a Kerr black hole (BH). We find that the GFR effect changes the initial polarization state of the lensed GW. Compared with the Einstein deflection angle, the dominant term of the rotation angle $χ_g$ is a second-order correction to the polarization angle, which depends on the light-of-sight co…
Satellite tracking involves sending electromagnetic signals to Earth. Both the orbit of the spacecraft and the electromagnetic signals themselves are affected by the curvature of spacetime. The arrival time of the pulses is compared to the ticks of local clocks to reconstruct the orbital path of the satellite to high accuracy, and to implicitly measure general relativistic effects. In particular, Schwarzschild space curvature (static) and frame-dragging (stationary) due to the planet's spin affect the satellite's orbit. The dominant relativistic effect on the path of the signal photons is Shap…
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…
Newtonian simulations are routinely used to examine the matter dynamics on non-linear scales. However, even on these scales, Newtonian gravity is not a complete description of gravitational effects. A post-Friedmann approach shows that the leading order correction to Newtonian theory is a vector potential in the metric. This vector potential can be calculated from N-body simulations, requiring a method for extracting the velocity field. Here, we present the full details of our calculation of the post-Friedmann vector potential, using the Delauney Tesselation Field Estimator (DTFE) code. We inc…
General relativistic effects in the weak field approximation are calculated for electromagnetic Laguerre-Gaussian (LG) beams. The current work is an extension of previous work on the precession of a spinning neutral particle in the weak gravitational field of an optical vortex. In the current work, the metric perturbation is extended to all coordinate configurations and includes gravitational effects from circular polarization and intrinsic hyperbolic momentum. The final metric reveals frame-dragging effects due to intrinsic spin angular momentum (SAM), orbital angular momentum (OAM), and spin…
It has been expected that astronomical observations to detect the orbital angular momenta of electromagnetic waves may give us a new insight into astrophysics. Previous works pointed out the possibility that a rotating black hole can produce orbital angular momenta of electromagnetic waves through gravitational scattering, and the spin parameter of the black hole can be measured by observing them. However, the mechanism how the orbital angular momentum of the electromagnetic wave is generated by the gravitational scattering has not been clarified sufficiently. In this paper, in order to unders…
In this work, we elaborate on the development of a general relativistic formalism that allows one to analytically express the mass and spin parameters of the Kerr black hole in terms of observational data: the total redshift and blueshift of photons emitted by geodesic massive particles revolving the black hole and their orbital parameters. Thus, we present concise closed formulas for the mass and spin parameters of the Kerr black hole in terms of few directly observed quantities in the case of equatorial circular orbits either when the black hole is static or is moving with respect to a dista…
The transformation of powerful gravitational waves, created by the coalescence of massive black hole binaries, into electromagnetic radiation in external magnetic fields is revisited. In contrast to the previous calculations of the similar effect, we study the realistic case of the gravitational radiation frequency below the plasma frequency of the surrounding medium. The gravitational waves propagating in the plasma constantly create electromagnetic radiation dragging it with them, despite the low frequency. The plasma heating by the unattenuated electromagnetic wave may be significant in a h…
The Australian National University（澳大利亚国立大学）；Perimeter Institute for Theoretical Physics（理论物理珀米特研究所）；Universitat de les Illes Balears（巴利阿里群岛大学）；California Institute of Technology（加州理工学院）
We elucidate the dynamics of a thin spherical material shell with a tangential pressure, using a new approach. This is both simpler than the traditional method of extrinsic curvature junction conditions (which we also employ), and suggests an expression for a `gravitational potential energy' of the shell. Such a shell, if slowly spinning, can rotationally drag the inertial frames within it through a finite angle as it collapses and rebounds from a minimum radius. Rebounding `spherical' and cylindrical pulses of rotating gravitational waves were studied previously. Here we calculate their angul…
The frame-dragging vector potential on galaxy scales from Dark-Matter-only Newtonian $N$-body simulations
INAF - Osservatorio Astrofisico di Torino（意大利国家天体物理研究所都灵天文台）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）；INFN Sezione di Trieste（意大利国家核物理研究所里雅斯特分部）；Instituto de Física y Astronomía, Universidad de Valparaíso（瓦尔帕莱索大学物理与天文学研究所）
Since the first appearance of general relativity in 1916, various experiments have been conducted to test the theory. Due to the weakness of the interactions involved, all of the documented tests were carried out in a gravitational field generated by objects of an astronomical scale. We propose an idea for an experiment that could detect purely general-relativistic effects in a lab-generated gravitational field. It is shown that a set of dense rapidly-revolving cylinders produce a frame-dragging effect substantial enough to be two orders of magnitude away from the observable range of the next …
The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of dynamical and kinematic equations governing the matter coupling and evolution of the electric and magnetic parts of the Weyl tensor, so-called gravitoelectric and gravitomagnetic fields. A detailed analysis of the Weyl gravitoelectromagnetic fields can be conducted using a number of algebraic and d…
Merging compact black-hole (BH) binaries are likely to exist in the nuclear star clusters around supermassive BHs (SMBHs), such as Sgr A$^\ast$. They may also form in the accretion disks of active galactic nuclei. Such compact binaries can emit gravitational waves (GWs) in the low-frequency band (0.001-1 Hz) that are detectable by several planned space-borne GW observatories. We show that the orbital axis of the compact binary may experience significant variation due to the frame-dragging effect associated with the spin of the SMBH. The dynamical behavior of the orbital axis can be understood …
The magnetic field due to an axially symmetric, hot and highly conducting plasma, taken as an ideal magnetohydrodynamic fluid, surrounding a slow rotating compact gravitational object is studied within the context of Einstein-Maxwell field equations. It is assumed that whereas the plasma is effected by the background spacetime it does not effect the spacetime itself. The Einstein-Maxwell equations are then solved for the magnetic field in a comoving frame with the background spacetime described by the slow rotating Kerr black hole spacetime. It is found that the solutions are magnetic waves tr…
