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} corrections. The transition to a chaotic behavior strictly depends on the initial conditions. The orbital phase space portrait is discussed.
The dynamics of fluid-matter under the influence of gravitomagnetic fields are formulated and solved for the case of fully developed turbulence. Gravitomagnetic effects reduce the vortical complexity and nonlinearity of turbulence, even leading to its extinction within large volumes, and generate departures from Kolmogorov turbulence scalings, that are explained via a combination of dimensional and exact analysis arguments.
We show that the motion of the neutral masses in an accretion disk orbiting a black hole creates a general-relativistic magnetic-like (gravitomagnetic) field that vertically accelerates neutral particles near the accretion disk upward and then inward toward the axis of the accretion disk. Even though this gravitomagnetic field alone does not achieve collimated jets, it is a novel means to identify one general relativistic effect from a much more complicated problem. In addition, as the accelerated material above or below the accretion disk nears the axis with a nearly vertical direction, a fra…
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 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…
In General Relativity, the rotation of a gravitating body like the Earth influences the motion of orbiting test particles or satellites in a non-Newtonian way. This causes, e.g., a precession of the orbital plane known as the Lense-Thirring effect and a precession of the spin of a gyroscope known as the Schiff effect. Here, we discuss a third effect first introduced by Cohen and Mashhoon called the gravitomagnetic clock effect. It describes the difference in proper time of counterrevolving clocks after a revolution of $2π$. For two clocks on counterrotating equatorial circular orbits around th…
In the framework of the so-called gravitoelectromagnetic formalism, according to which the equations of the gravitational field can be written in analogy with classical electromagnetism, we study the gravitomagnetic field of a rotating ring, orbiting around a central body. We calculate the gravitomagnetic component of the field, both in the intermediate zone between the ring and the central body, and far away from the ring and central body. We evaluate the impact of the gravitomagnetic field on the motion of test particles and, as an application, we study the possibility of using these results…
We analytically work out the orbital effects induced by the gravitomagnetic spin-octupole moment of an extended spheroidal rotating body endowed with angular momentum $\boldsymbol{S}$ and quadrupole mass moment $J_2$. Our results, proportional to $S J_2 c^{-2}$, hold for an arbitrary orientation of the body's symmetry axis $\boldsymbol{\hat{S}}$ and a generic orbital configuration of the test particle. Such effects may be measurable, in principle, with a dedicated spacecraft-based mission to Jupiter. For a moderately eccentric and fast path, the gravitomagnetic precessions of the node and the …
The effects of highly relativistic spin-gravity coupling in the Schwarzschild-de Sitter background which follow from the Mathisson-Papapetrou equations are investigated. The dependence of gravitoelectric and gravitomagnetic components of gravitational field on the velocity of an observer which is moving in Schwarzschild-de Sitter's background is estimated. The action of gravitomagnetic components on a fast moving spinning particle is considered. Different cases of the highly relativistic circular orbits of a spinning particle which essentially differ from the corresponding geodesic orbits are …
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…
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…
First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data
We show that the gravitomagnetic interaction of a Kerr black hole (BH) with a surrounding magnetic field induces an electric field that accelerates charged particles to ultra-relativistic energies in the vicinity of the BH. Along the BH rotation axis, these electrons/protons can reach energies of even thousands of PeV, so stellar-mass BHs in long gamma-ray bursts (GRBs) and supermassive BHs in active galactic nuclei (AGN) can contribute to the ultrahigh-energy cosmic rays (UHECRs) thorough this mechanism. At off-axis latitudes, the particles accelerate to energies of hundreds of GeV and emit s…
A supermassive black hole moving through a field of stars will gravitationally scatter the stars, inducing a backreaction force on the black hole known as dynamical friction. In Newtonian gravity, the axisymmetry of the system about the black hole's velocity $\mathbf{v}$ implies that the dynamical friction must be anti-parallel to $\mathbf{v}$. However, in general relativity the black hole's spin $\mathbf{S}$ need not be parallel to $\mathbf{v}$, breaking the axisymmetry of the system and generating a new component of dynamical friction similar to the Lorentz force $\mathbf{F} = q\mathbf{v} \t…
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…
