Dragging of inertial frames by matter and waves

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.

Gravitomagnetic vorticity generation in black hole accretion disks: a potential spatial constraint on plasma flow stability

We calculate the vorticity generation rate in the accretion disk near a slowly rotating black hole in the low velocity, weak-field limit of general relativity. Specifically, we find that the frame-dragging effect due to the black hole’s rotation – manifested through the gravitomagnetic field – can generate vorticity in a moving plasma in the accretion disk. The mechanism remains operational as long as the accretion disk has non-negligible vertical height and is independent of the exact thermodynamical profile of the disk. The enstrophy density generation rate, as a measure of turbulence and dissipation, is presented, which indicates that the frame-dragging effect can disrupt the stability of the disk away from the z = 0 plane.

Inductive Rectilinear Frame Dragging and Local Coupling to the Gravitational Field of the Universe

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. The drag force can be understood as inductive rectilinear frame dragging because it also exists in the rest frame of a moving object, and it arises in that frame from the off-diagonal components induced in the boosted-frame metric. Unlike the Kerr metric or other typical frame-dragging geometries, cosmological inductive dragging occurs at uniform velocity, along the direction of motion, and dissipates energy. Proposed gravito-magnetic invariants formed from contractions of the Riemann tensor do not capture inductive dragging effects, and this might be the first identification of inductive rectilinear dragging. The existence of this drag force proves it is possible for matter in motion through a finite region to exchange momentum and energy with the gravitational field of the universe. The cosmological metric can in principle be determined through this force from local measurements on moving bodies, at resolutions similar to that of the Pound–Rebka experiment.

Towards communication in a curved spacetime geometry

The current race in quantum communication – endeavouring to establish a global quantum network – must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10 radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism; can cause a 12.2% cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information.

Path Tracing Photons Oscillating Through Alternate Universes Inside a Black Hole

In case of the maximally rotating Black Holes (BH) through Kerr-Neumann frames, or as described in Boyer-Lindquist coordinates metrics, the rotation axis of the BHs inputs a frame dragging effect i.e., relativistically a Lens-Thirring Precession that accelerates the photon trajectories oscillates with a shaped induced rotations through the ring singularity, between alternate universes, as a means of an induced geodesics that takes a sharp turning points back and forth provided, in the prograde photon sphere, due to magnetorotational instability, the path tracing of a photons circulates as a smooth fiber bundles over the event horizon curves, that when gets interpolate between mixed trajectories behaves as a geodesics and thus forms a smooth Jacobi-fields through Jacobi-lines by mutual intersection of geodesics over the photon sphere which when somehow gets leaked inside the event horizon, then gets sucked in with not sufficient escape velocity for retardation and trapped in the compact singularity, oscillating back and forth through alternate universes.

General relativistic aberration equation and measurable angle of light ray in Kerr spacetime

We will mainly discuss the measurable angle (local angle) of the light ray [Formula: see text] at the position of the observer [Formula: see text] instead of the total deflection angle (global angle) [Formula: see text] in Kerr spacetime. We will investigate not only the effect of the gravito-magnetic field or frame dragging due to the spin of the central object but also the contribution of the motion of the observer with a coordinate radial velocity [Formula: see text] and a coordinate transverse velocity [Formula: see text] where [Formula: see text] is the impact parameter ([Formula: see text] and [Formula: see text] are the angular momentum and the energy of the light ray, respectively) and [Formula: see text] is a coordinate angular velocity. [Formula: see text] and [Formula: see text] are computed from the components of the four-velocity of the observer [Formula: see text] and [Formula: see text], respectively. Because the motion of observer causes an aberration, we will employ the general relativistic aberration equation to obtain the measurable angle [Formula: see text] which is determined by the four-momentum of the light ray [Formula: see text] and the four-momentum of the radial null geodesic [Formula: see text] as well as the four-velocity of the observer [Formula: see text]. The measurable angle [Formula: see text] given in this paper can be applied not only to the case of the observer located in an asymptotically flat region but also to the case of the observer placed within the curved and finite-distance region. Moreover, when the observer is in radial motion, the total deflection angle [Formula: see text] can be expressed by [Formula: see text]; this is consistent with the overall scaling factor [Formula: see text] instead of [Formula: see text] with respect to the total deflection angle [Formula: see text] in the static case ([Formula: see text] is the velocity of the lens object). On the other hand, when the observer is in transverse motion, the total deflection angle is given by the form [Formula: see text] if we define the transverse velocity as having the form [Formula: see text].

Haynes 242 Alloy for Lares 2 Satellite

The satellite LARES 2 is designed to test dragging of inertial frames, or frame-dragging, predicted by Einstein’s theory of General Relativity, with accuracy of a few parts in a thousand. For this purpose, besides the typical requirements for a space construction, a high density alloy must be used. In this paper are reported the studies performed on a nickel alloy, the Haynes 242, that is considered a possible candidate for manufacturing all the metallic parts of LARES 2 and other passive geodetic satellites. Haynes 242 density and mechanical properties are compliant with the requirements of the mission. Three different casting with the nominal composition of the alloy have been prepared and tested along with a commercial bar of Haynes 242. The results of tensile and hardness tests on several specimens with different aging time are reported, along with the relevant metallographic analysis. Furthermore, a test on the machinability, performed on a screw, which is the most demanding item from the manufacturing point of view, is reported.