Frame-dragging Research Articles

Gravitomagnetism and status of the LAGEOS III experiment

After an introduction on the meaning of gravitomagnetism and dragging of inertial frames, and a characterization of gravitomagnetism with curvature invariants, we present an updated review of the LAGEOS III experiment to measure the gravitomagnetic field with two non-polar, passive, laser ranged satellites with supplementary inclinations.

A general relativistic toroid around a black hole

view Abstract Citations (48) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A General Relativistic Toroid around a Black Hole Nishida, Shogo ; Eriguchi, Yoshiharu Abstract We present a powerful new numerical method to obtain the equilibrium states of a toroid around a black hole. The integral representation of Einstein's equations used in this paper has several advantages, one of which is that it can easily take into account the asymptotic behavior of the metric. This computational scheme can be applied to configurations with any strength of gravity of toroids and any amount of rotation of black holes. By using this scheme, we have obtained many new equilibrium configurations of general relativistic thick toroids. Highly relativistic effects of toroids on black holes or on external spacetimes have been investigated. In particular, dragging of inertial frames and tidal forces due to toroids can be clearly seen by studying the angular momentum of a black hole when the mass of the toroid is varied. Some black holes are found to have an ergoregion even if their angular momentum is zero. We find that the shape of a black hole becomes spherical when its angular momentum vanishes, even if a massive toroid exists around it. From this result, we can define nonrotating or 'spherical' black holes as those which have zero angular momentum irrespective of their angular velocity. We can, therefore, extract energy from spherical black holes, because spherical black holes can have an ergoregion. Furthermore, our schemes and results will contribute to the study of the stability of relativistic self-gravitating thick toroids by allowing the investigation of circular orbits of free particles around black holes. Publication: The Astrophysical Journal Pub Date: May 1994 DOI: 10.1086/174153 Bibcode: 1994ApJ...427..429N Keywords: Accretion Disks; Applications Of Mathematics; Black Holes (Astronomy); Equilibrium Methods; Relativity; Toroids; Angular Momentum; Angular Velocity; Circular Orbits; Gravitation; Inertial Reference Systems; Planetary Temperature; Astrophysics; ACCRETION; ACCRETION DISKS; BLACK HOLE PHYSICS; RELATIVITY full text sources ADS |

Rotational perturbations and frame dragging in a Friedmann universe

Classical work on frame dragging effects near a slowly rotating mass shell and later improvements thereof are extended to a model with cosmological boundary conditions: a mass shell with flat interior in an asymptotic Friedmann universe. The metric describing a shell, which follows the motion of the surrounding cosmic dust, can be given in terms of analytic functions. Its energy-momentum tensor fulfils the energy conditions. Rotation of the shell and the cosmic matter is treated in the first order of the angular velocity and a perturbation of this exact solution. The dragging of the inertial frames inside the shell is defined in an invariant manner by, in principle, measurable quantities. It is shown that frame dragging occurs in this rotationally perturbed Friedmann universe and that the inertial frames are influenced by the shell as well as by the cosmic matter. The behaviour of the dragging coefficient is discussed and compared with results of previous work.

Gravity Probe B Gyroscope charge control using field-emission cathodes

We propose and test a method for controlling the charging of the Gravity Probe B(GP-B) electrostatically suspended gyroscopes using electrons generated by field emission cathodes. The GP-B Gyroscope Experiment is designed to measure for the first time the geodetic and the frame-dragging effects predicted by Einstein’s general theory of relativity. The expected accuracy of ∼0.3 marcsec/yr (10−11 deg/h) will allow for a 0.01% measurement of the geodetic effect and a 1% measurement of the frame-dragging effect. Gyroscope charging is caused by cosmic radiation, by field emission, and by the separation of dissimilar metals. The expected charging rate for the gyroscopes is ∼1 nC/yr and consequently above the 50 pC limit dictated by disturbing torque considerations. The present charge control technique is based on ultraviolet photoemission of electrons from both the gyroscope and an auxiliary electrode. Experiments have shown this method to be effective at room temperature in ground testing, and calculations indicate that it is suitable for charge control in orbit. As an alternative we demonstrate the use of Spindt-type field emission cathodes for the control of the positive charges on the gyroscopes, by using a 10 000 tip emitter array produced by SRI International. The device requirements are (a) stable and reliable operation over two years at 2 K and 1.5×10−9 Pa, (b) average power dissipation in the device of less than 50 μW, (c) peak emission current of 1–100 pA, (d) dimensions less than 2 mm, (e) magnetization less than 10−8 G, (f) electric field at the gyroscope less than 104 V/m. The control of negative charges on the gyroscope is achievable by operating in a regime in which the secondary electron emission coefficient is greater than unity.

Effects of a self-gravitating disc on test particle motion around a Kerr black hole

The nature of test particle motion in the presence of a rotating ring of self-gravitating matter around a Kerr black hole is studied. A pseudo-Kerr potential is used to describe the rotating hole. The result shows that, as the mass of the disc is increased, the radius of the marginally bound orbit decreases, whereas the location of the marginally stable orbit, as well as the maximum fraction of the binding energy that can be released, increases. The Keplerian angular momentum distribution, the effects due to dragging of inertial frames by the rotating ring and the force acting on a test particle are also studied

The Effect of Light Bending and Redshift on Pulsar Beaming: The Case of Shorter Rotation Periods

AbstractAn estimate of the effect of light bending and redshift on pulsar beam characteristics has been made using a weak Kerr metric for the case of a 1.4 M⊙ neutron star with a radius in the range 6-10 km and rotation periods of 1.56 ms and 33 ms, respectively. Assuming that the pulsar emission has the form of a narrow conical beam directed away from the surface and is located within two stellar radii, the beam is found to be widened by a factor of ≤ 2 and to suffer a reduction in the intensity (flattening of the profile) by an order of magnitude or less. The effect is largest for the most rapidly rotating the neutron stars. For an emission region located beyond 20 km, the flattening is generally insignificant. The pulse profile is slightly asymmetrical due to dragging of the inertial frames. For millisecond periods, aberration tends to reverse the flattening effect of space-time curvature by narrowing the pulse and can completely overcome it for emission from a location beyond ≃30km. Although the pulse must slightly brighten up, a large redshift factor overcomes this effect to keep the pulse flattened for all neutron star radii considered here.

General Relativistic Electrodynamics of the Magnetic Polar Regions of Neutron Stars

AbstractThe induction of the electric fields near a rotating neutron star is considered within the framework of General Relativity. It is demonstrated that within the open magnetic field region, filled by relativistically moving charged particles, a sufficiently strong component of the electric field is generated. This component is due to the effect of dragging of inertial frames of reference and predominates in the case when a neutron star is not exactly an orthogonal rotator. Finally, we discuss some implications of our results on the theory of radio pulsars.

Dragging of inertial frames by a charged magnetic dipole

Dragging of inertial frames is normally associated with rotating bodies. I consider here a static massive charged magnetic dipole, and show that its gravitational field drags inertial frames, and causes gyroscopes to precess. A numerical estimate of the effect is given, and an experiment is suggested.

Self-interaction of a point charge in a Kerr spacetime

As is known, the expression of the electromagnetic field from a charge at rest on the symmetry axis of a Kerr spacetime, first given as a multi-polar expansion, has been later calculated in closed form. This allowed the derivation, in closed form, of the electromagnetic 4-potential and, consequently, the electrostatic self-interaction force (“self-force”) on the charge. We point out that, in order to derive the electromagnetic 4-potential and, consequently, the electrostatic self-force, a particular reference frame is required, in which the Kerr metric “locally” (i.e., in a small neighbourhood of the charge world-line) reduces to that of a static homogeneous gravitational field (SHGF). The starting point of this paper is the realization that the choice of such a reference frame in the literature is incorrect, because the phenomenon of dragging of inertial frames is neglected. This demands a new derivation both of the electromagnetic 4-potential and of the electrostatic self-force. To this end, we construct the correct reference frame, “locally“ transforming the Kerr metric into that of an SHGF. In such a frame, we derive the correct expressions both of the electromagnetic 4-potential and of the electrostatic self-force. In particular: i) the time component of the 4-potential differs from that known in the literature by an additional term, induced by the dragging of inertial frames, vanishing only on the symmetry axis; ii) the self-force turns out to be the sum of two terms, of which only the first (involving both the mass and the angular momentum per unit mass of the Kerr spacetime) is known in the literature. The second term (involving only the angular momentum per unit mass), which arises from a careful calculation and not from the additional term in the 4-potential, is a significant improvement provided by this paper.

Rotational perturbations of relativistic perfect-fluid model universes interacting with gravitational field

Along with the presentation of several new analytic solutions, the dynamics of slowly rotating perfect-fluid model universes are investigated, and their physical and geometrical properties are discussed from all angles. The rotational perturbations of such models are examined in detail in order to substantiate the possibility that the Universe is endowed with some rotation. The nature and role of the rotational velocity Ω (r, t) which is related to the local dragging of inertial frames and that of the matter rotation ω(r, t) are studied for uniform and non-uniform motions. We find out the restrictions on the radii of the models for real astrophysical situations, and the periods of physical validity of them are also obtained. Rotating models which are expanding as well are obtained, in which cases the rotational velocities are found to decay with the time; and these models may be taken as examples of real astrophysical objects in this Universe.

Geodetic precession or dragging of inertial frames?

In General Relativity, the Principle of General Covariance allows one to describe phenomena by means of any convenient choice of coordinate system. Here, it is shown that the geodetic precession of a gyroscope orbiting a spherically symmetric, nonrotating mass can be recast as a Lense-Thirring frame-dragging effect, in an appropriately chosen coordinate frame whose origin falls freely along with the gyroscope and whose spatial coordinate axes point in fixed directions.

Rotating magnetoviscous-fluid universes in general relativity

In the course of presentation of several new analytic solutions, the dynamics of slowly rotating magnetoviscous-fluid distribution is investigated. The nature and role of the rotational velocity Ω (r, t) which is related to the local dragging of inertial frames and that of matter rotation ω(r, t) are studied for uniform and non-uniform motions. It is observed that the magnetic field decays the rotational motion and this damping effect is found to be roughly analogous to viscosity. Rotating models which are expanding as well are obtained, which may be taken as good examples of real astrophysical situations; and their geometrical and physical properties are discussed in detail.

The Stellar X-Ray Polarimeter for the Spectrum-X-Gamma Mission

AbstractWe describe an X-ray polarimeter which will be flown on the SPECTRUM-X-Gamma mission. The instrument exploits three distinct physical processes to measure polarization: Bragg reflection from a graphite crystal, Thomson scattering from a metallic lithium target, and photoemission from a Cesium Iodide photocathode. These three processes allow polarization measurements over an energy band of 0.3 keV to 12 keV. The polarimeter will make possible sensitive measurements of several hundred known X-ray sources. X-ray polarization measurements will allow us to constrain the geometry of gas flow in X-ray binaries, identify nonthermal emission in supernova remnants, test current models for X-ray emission in radio pulsars, determine the radiation mechanisms in active galactic nuclei, and search for inertial frame dragging (Lense-Thirring effect) around the putative black hole in Cygnus X-1.

Stellar X-Ray Polarimeter: a focal plane polarimeter for the Spectrum X-Gamma mission

This paper describes an X-ray polarimeter that will be flown on the Spectrum X-Gamma mission. The instrument exploits three distinct physical processes to measure polarization: Bragg reflection from a graphite crystal, Thomson scattering from a metallic lithium target, and photoemission from a cesium iodide photocathode. These three methods allow polarization measurements over an energy band from 0.3 to 12 keV. The polarimeter will make possible sensitive measurements of several hundred known X-ray sources. X-ray polarization measurements will make it possible to constrain the geometry of gas flow in X-ray binaries, identify nonthermal emission in supernova remnants, test current models for X-ray emission in radio pulsars, determine the radiation mechanisms in active galactic nuclei, and search for inertial frame dragging (Lense-Thirring effect) around the putative black hole in Cygnus X-1.

Self-similar relativistic discs with pressure

Solutions for discs in equilibrium specified by a constant velocity of rotation and constant velocity dispersions are found. The fluid is not perfect because the stress tensor is anisotropic. These discs are self-similar if they are of infinite extent. The solutions are exact when an equal number of particles move in each sense of rotation so that there is no dragging of the inertial frames. For discs rotating with a small velocity a WKB approximation is used to obtain solutions.

On the use of clocks in satellites for the testing of dragging of inertial frames in Einstein's general relativity

It is shown that it is possible by using the lack of synchronization of clocks by light signal synchronization in circular orbits to test for the dragging of inertial frames in Einsteins's theory of general relativity. Possible experiments are discussed.

Clock transport synchronization and the dragging of inertial frames for elliptical orbits

It is shown that is is possible to test for the dragging of inertial frames in Einstein's theory of general relativity by using the discrepancy between clocks synchronized by clock transport in elliptical orbits. Possible experiments are discussed.

Gravitational light deflection and the dragging of inertial frames.

The gravitational field generated by currents of matter within a body influences the deflection of light by the body. We show that in metric theories of gravity the Einstein equivalence principle implies a deeper connection than had been realized between this deflection and the Lense-Thirring dragging of inertial frames.

Satellite test for dragging of inertial frames

It is shown that it is possible by using the lack of synchronization of clocks by light signal synchronization in elliptical orbits to test for the dragging of inertial frames in Einstein's theory of general relativity. Possible experiments are discussed.

Slowly-rotating charged viscous-fluid universes: Exact solutions

By considering a spherically-symmetric metric, certain new analytic solutions for charged rotating viscous-fluid cosmological models in the Einstein universe are found out. Five different cases in which the nature and role of the rotational velocity Ω(r, t) is related to the local dragging of inertial frames and that of matter rotation ω(r, t), are investigated. Except for the case of ‘perfect dragging’, the electric field is found to have a damping effect on the rotation of matter. The damping effect is seen to be roughly analogous to the viscosity. In some solutions we find out the temporal restrictions for realistic astrophysical situations. Models which are rotating as well as expanding are also obtained and studied.