Gravitational waveforms and production could be considerably affected by gravitomagnetic corrections considered in relativistic theory of orbits. Beside the standard periastron effect of General Relativity, new nutation effects come out when c^{-3} corrections are taken into account. Such corrections emerge as soon as matter-current densities and vector gravitational potentials cannot be discarded into dynamics. We study the gravitational waves emitted through the capture, in the gravitational field of massive binary systems (e.g. a very massive black hole on which a stellar object is inspiralling) via the quadrupole approximation, considering precession and nutation effects. We present a numerical study to obtain the gravitational wave luminosity, the total energy output and the gravitational radiation amplitude. From a crude estimate of the expected number of events towards peculiar targets (e.g. globular clusters) and in particular, the rate of events per year for dense stellar clusters at the Galactic Center (SgrA*), we conclude that this type of capture could give signatures to be revealed by interferometric GW antennas, in particular by the forthcoming laser interferometer space antenna LISA.
Several relativistic quantum gravitational effects such as spin-rotation coupling, gravitomagnetic charge and gravitational Meissner effect are investigated in the present letter. The field equation of gravitomagnetic matter is suggested and a static spherically symmetric solution of this equation is offered. With foreseeable improvements in detecting and measuring technology, it is possible for us to investigate quantum mechanics in weak-gravitational fields. The potential implications of these gravitational effects (or phenomena) to some problems are briefly discussed.
This essay discusses some geometric effects associated with gravitomagnetic fields and gravitomagnetic charge as well as the gravity theory of the latter. Gravitomagnetic charge is the duality of gravitoelectric charge (mass) and is therefore also termed the dual mass which represents the topological property of gravitation. The field equation of gravitomagnetic matter is suggested and a static spherically symmetric solution of this equation is offered. A possible explanation of the anomalous acceleration acting on Pioneer spacecrafts are briefly proposed.
We introduce the Gauge Vector-Tensor (GVT) theory by extending the AQUAL's approach to the GravitoElectroMagnetism (GEM) approximation of gravity. GVT is a generally covariant theory of gravity composed of a pseudo Riemannian metric and two U(1) gauge connections that reproduces MOND in the limit of very weak gravitational fields while remains consistent with the Einstein-Hilbert gravity in the limit of strong and Newtonian gravitational fields. GVT also provides a simple framework to study the GEM approximation to gravity. We illustrate that the gravitomagnetic force at the edge of a galaxy c…
The interaction of a plane gravitational wave with test masses can be described in the proper detector frame, using Fermi coordinates, in terms of a gravitoelectric and a gravitomagnetic field. We use this approach to calculate the displacements produced by gravitational waves up to second order in the distance parameter and, in doing so, we emphasize the relevance of the gravitomagnetic contribution related to gravitational induction. In addition, we show how this approach can be generalized to calculate displacements up to arbitrary order.
We show that using Fermi coordinates it is possible to describe the gravitational field of a wave using a gravitoelectromagnetic analogy. In particular, we show that using this approach, a new phenomenon, called gravitomagnetic resonance, may appear. We describe it both from classical and quantum viewpoints, and suggest that it could in principle be used as the basis for a new type of gravitational wave detectors.
Vacuum polarization in QED in a background gravitational field induces interactions which {\it effectively} modify the classical picture of light rays as the null geodesics of spacetime. After a short introduction on the main aspects of the quantum gravitational optics, as a nontrivial example, we study this effect in the background of NUT space characterizing the spacetime of a spherical mass endowed with a gravitomagnetic monopole charge, the so called NUT factor.
The physically interesting gravitational analogue of magnetic monopole in electrodynamics is considered in the present paper. The author investigates the field equation of gravitomagnetic matter, and the exact static cylindrically symmetric solution of field equation as well as the motion of gravitomagnetic charge in gravitational fields. Use is made of the mechanism of gravitational Meissner effect, a potential interpretation of anomalous, constant, acceleration acting on the Pioneer 10/11, Galileo and Ulysses spacecrafts is also suggested.
Corrections to the relativistic orbits are studied considering higher order approximations induced by gravitomagnetic effects. We discuss in details how such corrections come out taking into account magnetic components in the weak field limit of gravitational field and then the theory of orbits is developed starting from the Newtonian one, the lowest order in the approximation. Finally, the orbital structure and the stability conditions are discussed giving numerical examples. Beside the standard periastron corrections of General Relativity, a new nutation effect is due to the c^{-3} correctio…
By using the Gauss-Bonnet theorem, the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime has been recently discussed, especially by taking account of the finite distance from a lens object to a light source and a receiver [Ishihara, Suzuki, Ono, Asada, Phys. Rev. D 95, 044017 (2017)]. We discuss a possible extension of the method of calculating the bending angle of light to stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we consider the light rays on the equatorial plane in the axisymmetric spacetime. We introduce a spati…
Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the ${\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gra…
Gravitational waves emitted by coalescing binary systems containing neutron stars (or other compact objects) carry signatures of the stars' internal equation of state, notably, through the influence of tidal deformations during the binary's inspiral stage. While the leading-order tidal effects for post-Newtonian binaries of compact bodies in general relativity are due to the bodies' mass-quadrupole moments induced by gravitoelectric tidal fields, we consider here the leading effects due to current-quadrupole moments induced by gravitomagnetic tidal fields. We employ an effective action approac…
The nature of Mashhoon's spin-rotation coupling is the interaction between a particle spin (gravitomagnetic moment) and a gravitomagnetic field. Here we will consider the coupling of graviton spin to the weak gravitomagnetic fields by analyzing the Lagrangian density of weak gravitational field, and hence study the purely gravitational generalization of Mashhoon's spin-rotation couplings.
After an introduction emphasizing the importance of the gravitomag- netic effect in general relativity, with a resume of some space-based appli- cations, we discuss the so-called magnetic components of gravitational waves (GWs), which have to be taken into account in the context of the total response functions of interferometers for GWs propagating from ar- bitrary directions.
We derive the delay in travel time of photons due to the spin of a body both inside a rotating shell and outside a rotating body. We then show that this time delay by the spin of an astrophysical object might be detected in different images of the same source by gravitational lensing; it might be relevant in the determination of the Hubble constant using accurate measurements of the time delay between the images of some gravitational lens systems. The measurement of the spin-time-delay might also provide a further observable to estimate the dark matter content in galaxies, clusters, or super-c…
We study the gravitational time delay in ray propagation due to rotating masses in the linear approximation of general relativity. Simple expressions are given for the gravitomagnetic time delay that occurs when rays of radiation cross a slowly rotating shell and propagate in the field of a distant rotating source. Moreover, we calculate the local gravitational time delay in the Goedel universe. The observational consequences of these results in the case of weak gravitational lensing are discussed.
Gravitational waves (GWs) from binary neutron stars (NSs) have opened unique opportunities to constrain the nuclear equation of state by measuring tidal effects associated with the excitation of characteristic modes of the NSs. This includes gravitomagnetic modes associated with the Coriolis effect, whose frequencies are proportional to the NS's spin frequency, and for which the spin orientation determines the subclass of modes that are predominantly excited. We advance the GW models for these effects that are needed for data analysis by first developing a description for the adiabatic signatu…
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, t…
The paper summarizes the most important effects in Einsteinian gravitomagnetic fields related to propagating light rays, moving clocks and atoms, orbiting objects, and precessing spins. Emphasis is put onto the gravitational interaction of spinning objects. The gravitomagnetic field lines of a rotating or spinning object are given in analytic form.
Three weak gravitational effects associated with the gravitomagnetic fields are taken into account in this paper: (i) we discuss the background Lorentz transformation and gauge transformation in a linearized gravity theory, and obtain the expression for the spin of gravitational field by using the canonical procedure and Noether theorem; (ii) we point out that by using the coordinate transformation from the fixed frame to the rotating frame, it is found that the nature of Mashhoon's spin-rotation coupling is in fact an interaction between the gravitomagnetic moment of a spinning particle and t…
The electromagnetic measurements of general relativistic gravitomagnetic effects which can be performed within a conductor embedded in the space-time of slow rotating gravitational object in the presence of magnetic field are proposed.
In order to detect the gravitomagnetic clock effect by means of two counter-orbiting satellites placed on identical equatorial and circular orbits around the Earth with radius 7000 km their radial and azimuthal positions must be known with an accuracy of delta r =10^{-1} mm and delta phi =10^{-2} mas per revolution. In this work we investigate if the radial and azimuthal perturbations induced by the dynamical and static parts of the Earth' s gravitational field meet this requirements. While the radial direction is affected only by harmonic perturbations with periods up to some tens of days, th…
The quantization of the extended canonical momentum in quantum materials including the effects of gravitational drag is applied successively to the case of a multiply connected rotating superconductor and superfluid. Experiments carried out on rotating superconductors, based on the quantization of the magnetic flux in rotating superconductors, lead to a disagreement with the theoretical predictions derived from the quantization of a canonical momentum without any gravitomagnetic term. To what extent can these discrepancies be attributed to the additional gravitomagnetic term of the extended ca…
Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by tidal effects during a binary inspiral, leading to a potentially measurable effect in the gravitational-wave signal. We take an important step towards incorporating these effects in waveform models by developing a relativistic effective action for the gravitomagnetic dynamics that clarifies a number of subtleties. Working in the slow-rotation limit, we first consider the post-Newtonian approximation and explicitly derive the effective action from the equations of motion. We demonstrate that this formulation opens a w…
The analogy between general relativity and electromagnetism suggests that there is a galvano-gravitomagnetic effect, which is the gravitational analog of the Hall effect. This new effect takes place when a current carrying conductor is placed in a gravitomagnetic field and the conduction electrons moving inside the conductor are deflected transversally with respect to the current flow. In connection with this galvano-gravitomagnetic effect, we explore the possibility of using current carrying conductors for detecting the gravitomagnetic field of the Earth.
The gravitomagnetic corrections to the Keplerian period for a circular, geodesic orbit of a test particle in a polar plane containing the proper angular momentum J of a central rotating body are considered.
The detection of some tiny gravitomagnetic effects in the field of the Earth by means of artificial satellites is a very demanding task because of the various other perturbing forces of gravitational and non-gravitational origin acting upon them. Among the gravitational perturbations a relevant role is played by the Earth solid and ocean tides. In this communication I outline their effects on the detection of the Lense-Thirring drag of the orbits of LAGEOS and LAGEOS II, currently analyzed, and the proposed GP-C experiment devoted to the measurement of the clock effect.
Local conformal symmetry introduces the conformal curvature (Weyl tensor) that gets split into its (gravito-) electric and magnetic (tensor) parts. Newtonian tidal forces are expected from the gravitoelectric field, whereas general-relativistic frame-dragging effects emerge from the gravitomagnetic field. The symmetric, traceless gravitoelectric and gravitomagnetic tensor fields can be visualized by their eigenvectors and eigenvalues. In this essay, we depict the gravitoelectric and gravitomagnetic fields around a slowly rotating black hole. This suggests that the phenomenon of ultra-fast outf…
We study the gravitomagnetic effect in the context of absolute parallelism with the use of a modified geodesic equation via a free parameter b. We calculate the time difference in two atomic clocks orbiting the Earth in opposite directions and find a small correction due to the coupling between the torsion of the spacetime and the internal structure of atomic clocks measured by the free parameter.
Experimental discovery of the gravitomagnetic fields generated by translational and/or rotational currents of matter is one of primary goals of modern gravitational physics. The rotational (intrinsic) gravitomagnetic field of the Earth is currently measured by the Gravity Probe B. The present paper makes use of a parametrized post-Newtonian (PN) expansion of the Einstein equations to demonstrate how the extrinsic gravitomagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay caused by a moving gravitational lens. We prove that me…
Due to the resemblance between Maxwell and the gravitomagnetic equations obtained in the weak field and slow motion limit of General Relativity, one can ask if it is possible to amplify a seed intrinsic rotation or spin motion by a gravitomagetic dynamo, in analogy with the well-known dynamo effect. Using the Galilean limits of the gravitomagnetic equations, the answer to this question is negative, due to the fact that a "magnetic" Galilean limit for the gravitomagnetic equations is physically inconsistent. Also, we prove that, in spite of some claims, a gravitational Meissner effect does not …
The essence of the gravitomagnetic clock effect is properly defined showing that its origin is in the topology of world lines with closed space projections. It is shown that, in weak field approximation and for a spherically symmetric central body, the loss of synchrony between two clocks counter-rotating along a circular geodesic is proportional to the angular momentum of the source of the gravitational field. Numerical estimates are presented for objects within the solar system. The less unfavorable situation is found around Jupiter.
The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative Gravity (in flat space-time) named here as Maxwellian Gravity. The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian Gravity yields the gravitomagnetic moment of a Dirac (spin 1/2) particle exactly equals to its intrinsic spin. Violation of The Equivalence Principle (both at classical and quantum mechanical level) in the relativistic domain has also been reported in this work.
As a consequence of gravitomagnetism, which is a fundamental weak-field prediction of general relativity and ubiquitous in gravitational phenomena, clocks show a difference in their proper periods when moving along identical orbits in opposite directions about a spinning mass. This time shift is induced by the rotation of the source and may be used to verify the existence of the terrestrial gravitomagnetic field by means of orbiting clocks. A possible mission scenario is outlined with emphasis given to some of the major difficulties which inevitably arise in connection with such a venture.
The general relativistic gravitomagnetic clock effect consists in the fact that two massive test bodies orbiting a central spinning mass in its equatorial plane along two identical circular trajectories, but in opposite directions, take different times in describing a full revolution with respect to an asymptotically inertial observer. In the field of the Earth such time shift amounts to 10^{-7} s. Detecting it by means of a space based mission with artificial satellites is a very demanding task because there are severe constraints on the precision with which the radial and azimuthal positions…
Gravitomagnetic effects originates from the rotation of the source of the gravitational field and from the rotational features of the observers' frame. In recent years, gravitomagnetism has been tested by means of its impact on the precession of LAGEOS orbits and on the precession of spherical gyroscopes in the GP-B experiment. What we suggest here is that light can be used as a probe to test gravitomagnetic effects in an terrestrial laboratory: the proposed detector consists of large ring-lasers arranged along three orthogonal axes.
Propagation of light in the gravitational field of self-gravitating spinning bodies moving with arbitrary velocities is discussed. The gravitational field is assumed to be "weak" everywhere. Equations of motion of a light ray are solved in the first post-Minkowskian approximation that is linear with respect to the universal gravitational constant $G$. We do not restrict ourselves with the approximation of gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of source of light and observer. This formalism is applied for studying corrections to the Sha…
The well known general relativistic Lense-Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effec…
A compact binary system implicating at least one rotating neutron star undergoes gravitomagnetic tidal resonances as it inspirals toward its final merger. These have a dynamical impact on the phasing of the emitted gravitational waves. The resonances are produced by the inertial modes of vibration of the rotating star. Four distinct modes are involved, and the resonances occur within the frequency band of interferometric gravitational-wave detectors when the star spins at a frequency that lies within this band. The resonances are driven by the gravitomagnetic tidal field created by the compani…
The general relativistic gravitomagnetic clock effect involves a coupling between the orbital motion of a test particle and the rotation of the central mass and results in a difference in the proper periods of two counter-revolving satellites. It is shown that at O(c^-2) this effect has a simple analogue in the electromagnetic case. Moreover, in view of a possible measurement of the clock effect in the gravitational field of the Earth, we investigate the influence of some classical perturbing forces of the terrestrial space environment on the orbital motion of test bodies along opposite trajec…
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in earth's gravitational field may form a g…
In this paper we look at the gravitational spin--spin interaction between macroscopic astronomical bodies. In particular, we calculate their post--Newtonian orbital effects of order $\mathcal{O}(c^{-2})$ on the trajectory of a spinning particle with proper angular momentum ${\bf s}$ moving in the external gravitomagnetic field generated by a central spinning mass with proper angular momentum ${\bf J}$. It turns out that, at order $\mathcal{O}(e)$ in the orbiter's eccentricity, the eccentricity the pericenter and the mean anomaly rates of the moving particle are affected by long--term harmonic …
Linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations. For steady mass currents, this formalism has been used to understand gravitomagnetic effects like the Lense-Thirring dragging of inertial frames. For time-varying mass-energy currents, the analog of Faraday's law suggests new effects based on the gravitational equivalent of a transformer where such currents take the place of electrical currents. New experimental possibilities are suggested including…
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 …
Perturbations of satellite orbits in the gravitational field of a body with a mass monopole and arbitrary spin multipole moments are considered for an axisymmetric and stationary situation. Periodic and secular effects caused by the central gravitomagnetic field are derived by a first order perturbation theory. For a central spin-dipole field these results reduce to the well known Lense-Thirring effects.
This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the PN approximation and the further gravitomagnetic corrections. Finally by a classification of orbits in accordance with the conditions of motion, we calculate the gravitational waves luminosity for different types of stellar encounters and orbits.
We present here the proposal to use the LISA interferometer for detecting the gravito-magnetic field due to the rotation of the Milky Way, including the contribution given by the dark matter halo. The galactic signal would be superposed to the gravitomagnetic field of the Sun. The technique to be used is based on the asymmetric propagation of light along the closed contour of the space interferometer (Sagnac-like approach). Both principle and practical aspects of the proposed experiment are discussed. The strategy for disentangling the sought for signal from the kinematic terms due to proper r…
We compute gravitational self-force corrections to tidal invariants for spinning particles moving along circular orbits in a Schwarzschild spacetime. In particular, we consider the square and the cube of the gravitoelectric quadrupolar tidal tensor and the square of the gravitomagnetic quadrupolar tidal tensor. Our results are accurate to first-order in spin and through the 9.5 post-Newtonian order. We also compute the associated electric-type and magnetic-type eigenvalues.
The general relativistic kinetic theory including the effect of a stationary gravitational field is applied to the electromagnetic transport processes in conductors. Then it is applied to derive the general relativistic Ohm's law where the gravitomagnetic terms are incorporated. The total electric charge quantity and charge distribution inside conductors carrying conduction current in some relativistic cases are considered. The general relativistic Ohm's law is applied to predict new gravitomagnetic and gyroscopic effects which can, in principle, be used to detect the Lense-Thirring and rotati…
In this paper we consider the possibility of measuring the corrections induced by the square of the parameter a_g of the Kerr metric to the general relativistic deflection of electromagnetic waves and time delay in an Earth based experiment. It turns out that, while at astronomical scale the well known gravitoelectric effects are far larger than the gravitomagnetic ones, at laboratory scale the situation is reversed: the gravitomagnetic effects exceed definitely the gravitoelectric ones which are totally negligible. By using a small rapidly rotating sphere as gravitating source on the Earth th…
Beyond the Newtonian approximation, gravitational fields in general relativity can be described using a formalism known as gravitoelectromagnetism. In this formalism a vector potential, the gravitomagnetic potential, arises as a result of moving masses, in strong analogy with the magnetic force due to moving charges in Maxwell's theory. Gravitomagnetism can affect orbits in the gravitational field of a massive, rotating body. This raises the possibility that gravitomagnetism may serve as the dominant physics behind the anomalous rotation curves of spiral galaxies, eliminating the need for dark…
We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum ${\boldsymbol S}_\textrm{X}$ of a rotating mass $M_\textrm{X}$ orbited at distance $r_\textrm{X}$ by a local gravitationally bound restricted two-body system $\mathcal{S}$ of size $r\ll r_\textrm{X}$ consisting of a test particle revolving around a massive body $M$. At the lowest post-Newtonian order, we analytically work out the doubly averaged rates of change of the Keplerian orbital elements of the test particle by finding non-vanishing long-term effects for the inclination $I$, the node $Ω$ a…
