Covariant Anomaly and Hawking Radiation from Kerr-Newman Black Hole in Dragging Coordinates Frame

In the light of Robinson and Wilczek's new idea, and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole, we generally extend the work to Kerr-Newman black hole in dragging coordinates frame. It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame, which supports and extends Robinson and Wilczek's opinion.     

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor φ, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the n-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order c ⁻².     

Local gravitomagnetism

In a simple two-body system, we calculate the gravitomagnetic components of the metric in the local quasi-inertial frame of one of the bodies. The local geometry in this frame which is freely falling along the geodesic but is directionally fixed with respect to distant stars is primarily denned by the gravitomagnetic components of the local metric. This metric serves to track down the various contributions from the local and distant source and thus provides further insight to the nature of gravitomagnetism. As a result we show that in the quasi-inertial frame geodetic precession is a gravitomagnetic phenomenon. Furthermore we establish a connection between local gravitomagnetic effects and Einstein's principle of equivalence.     

Covariant Anomaly and Hawking Radiation from Kerr-Newman Black Hole in Dragging Coordinates Frame

in the light of Robinson and Wilczek＇s new idea, and motivated by Banerjee and Kulkarni＇s simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole, we generally extend the work to Kerr-Newman black hole in dragging coordinates frame. It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame, which supports and extends Robinson and Wilczek＇s opinion.     

New post-Newtonian parameter to test Chern-Simons gravity

We study Chern-Simons (CS) gravity in the parametrized post-Newtonian (PPN) framework through a weak-field solution of the modified field equations. We find that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional to the CS coupling and the curl of the PPN vector potential. This new term leads to a modification of frame dragging and gyroscopic precession and we provide an estimate of its size. This correction might be used in experiments, such as Gravity Probe B, to bound CS gravity and test string theory.     

Inertial Frame Dragging in an Acoustic Analogue Spacetime

We report an incipient exploration of the Lense‐Thirring precession effect in a rotating acoustic analogue black hole spacetime. An exact formula is deduced for the precession frequency of a gyroscope due to inertial frame dragging, close to the ergosphere of a ‘Draining Bathtub’ acoustic spacetime which has been studied extensively for acoustic Hawking radiation of phonons and also for ‘superresonance’. The formula is verified by embedding the two dimensional spatial (acoustic) geometry into a three dimensional one where the similarity with standard Lense‐Thirring precession results within a strong gravity framework is well known. Prospects of experimental detection of this new ‘fixed‐metric’ effect in acoustic geometries, are briefly discussed.     

Gravitomagnetic influence on gyroscopes and on the lunar orbit

Gravitomagnetism--a motional coupling of matter analogous to the Lorentz force in electromagnetism--has observable consequences for any scenario involving differing mass currents. Examples include gyroscopes located near a rotating massive body and the interaction of two orbiting bodies. In the former case, the resulting precession of the gyroscope is often called "frame dragging" and is the principal measurement sought by the Gravity Probe-B experiment. The latter case is realized in the Earth-Moon system, and the effect has in fact been confirmed via lunar laser ranging to approximately 0.1% accuracy--better than the anticipated accuracy of the Gravity-Probe-B result. This Letter shows the connection between these seemingly disparate phenomena by employing the same gravitomagnetic term in the equation of motion to obtain both gyroscopic precession and modification of the lunar orbit.     

Thomas Precession and the Bargmann-Michel-Telegdi Equation

A direct method showing the Thomas precession for an evolution of any vector quantity (a spatial part of a four-vector) is proposed. A useful application of this method is a possibility to trace correctly the presence of the Thomas precession in the Bargmann-Michel-Telegdi equation. It is pointed out that the Thomas precession is not incorporated in the kinematical term of the Bargmann-Michel-Telegdi equation, as it is commonly believed. When the Bargmann-Michel-Telegdi equation is interpreted in curved spacetimes, this term is shown to be equivalent to the affine connection term in the covariant derivative of the spin four-vector evolving in a gravitational field. It then contributes to the geodetic precession. The described problem is an interesting and unexpected example showing that approximate methods used in special relativity, in this case to identify the Thomas precession, can distort the true meaning of physical laws.     

Hawking radiation of dyon particles from the Einstein –Maxwell-Dilaton–Axion black hole via covariant anomaly

Hawking radiation of particles with electric and magnetic charges from the Einstein–Maxwell-Dilaton–Axion black hole is derived via the anomaly cancellation method, initiated by Robinson and Wilczek and elaborated by Banerjee and Kulkarni recently. We reconstruct the electromagnetic field tensor to redefine the gauge potential and equivalent charge corresponding to the source with electric and magnetic charges. We only adopt the covariant gauge and gravitational anomalies to discuss the near-horizon quantum anomaly in the dragging coordinate frame. Our result shows that Hawking radiation in this case also can be reproduced from the viewpoint of anomaly.     

Frame dragging with optical vortices

General Relativistic calculations in the linear regime have been made for electromagnetic beams of radiation known as optical vortices. These exotic beams of light carry a physical quantity known as optical orbital angular momentum. It is found that when a massive spinning neutral particle is placed along the optical axis, a phenomenon known as inertial frame dragging occurs. Our results are compared with those found previously for a ring laser and an order of magnitude estimate of the laser intensity needed for a precession frequency of 1 Hz is given for these “steady” beams of light.     

Hawking Radiation of Charged and Magnetized Particles from the Kerr-Newman-Kasuya Black Hole via Covariant Anomaly

Hawking radiation of a particle with electric and magnetic charges from the Kerr-Newman-Kasuya black hole is discussed in the dragging coordinate frame via the anomaly cancellation method, initiated by Robinson and Wilczek. We redefine an equivalent charge of the charged and magnetized black hole by reconstructing the electromagnetic field tensor. We adopt the refined covariant anomaly cancellation method to determining the compensating fluxes of charge flow and energy momentum tensor, which are proved to precisely match with those of the 2-dimensional blackbody radiation at the Hawking temperature with an appropriate chemical potential.     

Gyro precession and mach's principle

The precession of a gyroscope is calculated in a nonrelativistic theory due to Harbour which satisfies Mach's principle. It is shown that the theory predicts both the geodetic and motional precession of general relativity to within factors of order 1. The significance of the gyro experiment is discussed from the point of view of metric theories of gravity and this is contrasted with its significance from the point of view of Mach's principle.     

Detailed study of null and timelike geodesics in the Alcubierre warp spacetime

The geodesic equation of the Alcubierre warp spacetime is converted into its non-affinely parametrized form for a detailed discussion of the motion of particles and the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. To include gravitational lensing for point-like light sources, we present a practical approach using the Jacobi equation and the Sachs bases. Additionally, we consider the dragging and geodesic precession of particles due to the warp bubble.     

Gravitational Effects on the Vortex Distribution in Relativistic Superfluid Stars

Neutron stars are supposed to be mainly formed by a neutron superfluid. The angular momentum is given by the vortex array within the fluid, and a good account of the observable effects is determined by its coupling with the crust. In this article we show that the gravitational field introduces important modifications in the vortex distribution and shape. The inertial frame dragging on the quantum fluid produces a decrease in the vortex density, which for realistic models is in the order of 15%. This effect is relevant for neutron star rotation models and can provide a good framework for checking the quantum effect of the frame dragging.     

Hamiltonian approach to frame dragging

A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson–Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials.     

Machian Mechanics with Isotropic Inertia

A nonrelativistic theory is discussed here which contains an interaction which produces isotropic inertia for anisotropic matter distributions. The interaction is a 4-body interaction and it is explained why it is necessary to have this type of interaction. The consequences of the theory are discussed for celestial mechanics including the predicted perihelion precession. Frame dragging effects are calculated and compared with other theories. Possible ways to extend the theory to noninstantaneous interactions are briefly discussed. This theory demonstrates that Mach's principle in the form considered here is not necessarily inconsistent with isotropic inertia.     

Constraints on Kaluza–Klein gravity from Gravity Probe B

Using measurements of geodetic precession from Gravity Probe B, we constrain possible departures from Einstein’s General Relativity for a spinning test body in Kaluza–Klein gravity with one additional space dimension. We consider the two known static and spherically symmetric solutions of the 5D field equations (the soliton and canonical metrics) and obtain new limits on the free parameters associated with each. The theory is consistent with observation but must be “close to 4D” in both cases.     

Does Charge Contribute to the Frame Dragging of?Spacetime?

Electrically charged systems bound by a strong gravitational force can sustain a huge amount of electric charge (up to 10²⁰ C) against Coulomb repulsion. General relativistically such systems form a stable hydrostatic configuration both in the non-rotating and rotating cases. Here we study the effects of electric charge (electric energy density) on the spacetime outside a rotating electrically charged system bound by a strong gravitational force. In particular we investigate the effect of charge density on frame-dragging of spacetime in the exterior region. Using the coupled Einstein-Maxwell equations it is found that in the slow rotation approximation charge accumulation not only acts like an additional mass, thus modifying the spherically symmetric part of the spacetime, the electric charge also contributes directly to the dragging of spacetime. A modified Lense-Thirring formula for the spacetime frame dragging frequency is obtained and its implication for rotating charged compact stars is discussed.     

MTV-G experiment: Probing non-standard strong gravitational field at nuclear scale using geodetic precession

A new experiment named MTV-G, probing a large electron spin-precession due to a possible strong gravitational field, which predicted by large extra dimension model, is started at TRIUMF from 2011. In an electron-nuclear scattering experiment, a strong gravitational field is tested as a large spin precession effect caused by geodetic precession predicted by general relativity theory as a result of a warped space-time around nuclei. Experimental design using spin polarized electron source and Mott-spin analyzer, commissioning experiment and the preliminary results are described.