Translational inertial dragging

The electrical field inside a uniformly charged, slowly accelerated spherical shell is calculated. The result is used to find the inertial translational dragging field inside a slowly accelerated spherical shell of dust particles, according to the linearized gravitational field equations. The relevance of this effect in connection with Mach's principle and the principle of relativity is discussed.     

A Charged Rotating Cylindrical Shell

We give an example of a spacetime having an infinite thin rotating cylindrical shell constituted by a charged perfect fluid as a source. As the interior of the shell the Bonnor–Melvin universe is considered, while its exterior is represented by the Datta–Raychaudhuri spacetime. We discuss the energy conditions and we show that our spacetime contains closed timelike curves. Trajectories of charged test particles both inside and outside the cylinder are also examined. An expression for the angular velocity of a circular motion inside the cylinder is given.     

Slow rotation in the bimetric theory of gravitation

The equations describing the moment of inertia and the dragging of inertial frames of slowly rotating neutron stars are derived according to Rosen's bimetric theory of gravitation. Numerical calculations of the properties of neutron stars according to the bimetric theory and general relativity were made using several equations of state. The general trend found is that in the bimetric theory neutron stars with a given mass induce a smaller dragging of inertial frames than in general relativity. The moment of inertia of low-mass stars also is smaller in the bimetric theory. For high-mass stars, however, the moment of inertia is found to be larger in the bimetric theory.In partial fulfillment of the requirements for the D.Sc. degree.     

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.     

Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell

Vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field are investigated for the geometry of a wedge with a coaxial cylindrical boundary. All boundaries are assumed to be perfectly conducting, and both regions inside and outside the shell are considered. By using the generalized Abel–Plana formula, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry of the wedge without the cylindrical shell, and the second term is induced by the presence of the shell. The vacuum energy density induced by the shell is negative for the interior region and positive for the exterior region. The asymptotic behavior of the vacuum expectation values are investigated in various limiting cases. It is shown that the vacuum forces acting on the wedge sides due to the presence of the cylindrical boundary are always attractive. PACS 03.70.+k     

A Rotating Quantum Vacuum

We investigate how a uniformly rotating frame is defined as the rest frame of an observer rotating with constant angular velocity around the z axis of an inertial frame. Assuming this frame to be a Lorentz one, we second quantize a free massless scalar field in the rotating frame and obtain that creation-annihilation operators of the field are not the same as those of an inertial frame. This leads to a new vacuum state—a rotating vacuum. After this, introducing an apparatus device coupled linearly with the field, we obtain that there is a strong correlation between the number of Trocheries-Takeno particles (in a given state) obtained via canonical quantization and the response function of the rotating detector. Finally, we analyze polarization effects in circular accelerators in the proper frame of the electron, making a connection with the inertial frame point of view.     

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HL-2M vacuum vessel is designed with a D-shaped, double thin-wall structure, which consists of inner shell, outer shell, ribs and ports. Torus inside and outside diameters are 2m and 5.22m, respectively. Torus height is 3.02m. The whole torus will be welded with 20 sectors. Inconel 625 ??Inconel 718 and 316L are selected for the vessel material. Finite element analyses of vacuum vessel are conducted. The results show that vacuum vessel structure can meet the design requirements of the machine.     

High-energy approximations to nuclear scattering: W. E. Frahn and B. Schürmann. Physics Department,University of Cape Town,Rondebosch (Cape), South Africa

The effect of slow rotation on the dipole magnetic field of neutron stars is studied. It is shown that the differential rotation of inertial frames produced by the effect of “dragging of inertial frames” induces an additional component of electric field outside the star. This new component, as well as the usual electromagnetic components, vanishes as in the limit of collapse of a star to its Schwarzschild radius. For typical neutron stars, the electric quadrupole moment is about half that obtainable from a flat space analysis.     

关于Brueckner-Goldstone相连项展开公式

本文的目的是指明,倘满壳层外只有一个粒子或只含一个空穴,即使情态存有退化,我们仍可以求得消去了所有含有粒子自能图的项、而且在形式上和满壳层情况完全一样的相连项展开公式。     

Charged particle orbits in Kerr geometry with electromagnetic fields as viewed from locally non-rotating frames

The charged particle orbits in electromagnetic fields on Kerr background as viewed from a locally non-rotating frame do not exhibit non-gyrating bound orbits, which was an essential feature in the earlier study of Prasanna and Vishveshwara, thus showing the non gyration to be due to the effect of dragging of inertial frames produced by the rotating black hole.     

Casimir Forces for Robin Scalar Field on Cylindrical Shell in de Sitter Space

The Casimir stress on a cylindrical shell in background of conformally flat spacetime for massless scalar field is investigated. In the general case of Robin (mixed) boundary condition, formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the dS bulk is considered then different cosmological constants are assumed for the space inside and outside of the shell to have general results applicable to the case of cylindrical domain wall formations in the early universe.     

Spontaneous development of rotating inertial gravity wave inside the cylindrical tank with combined in- and outflow

A new phenomenon of the spontaneous development of the rotating inertial gravity wave inside the rigid cylindrical tank has been observed. The experimental set-up combines both the inflow and outflow. Three regimes of the flow inside the tank have been disclosed for the fixed rate of the liquid height change: a) nonrotating flow, b) nonrotating flow with the ripple localized to the tank’s wall, and c) emergence of the rotating inertial gravity wave. The rotating inertial gravity wave forces the fluid to rotate in the opposite direction. Each of these regimes is realized in some ranges of the outlet diameters and liquid heights, and the maps of these regimes are established.     

Casimir Energy for Spherical Shell in Schwarzschild Black Hole Background

In this paper, we consider the Casimir energy of massless scalar fields which satisfy the Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy.     

Scalar field quantization in stationary,non-static spacetimes

A quantization procedure is given for the scalar field on stationary, axisymmetric background spacetimes with orthogonal 2-surfaces. The procedure is based on observers orthogonal to surfaces of constant Killing time, and thus agrees with the usual procedure for static spacetimes. For stationary but nonstatic spacetimes the procedure differs from the usual one but nonetheless leads to a natural quantization scheme. Applying the procedure to flat space in rotating coordinates gives the standard, inertial Minkowski vacuum. For the Kerr spacetime, the procedure yields a particle definition which is well-defined everywhere outside the horizon. The above observers are just nonrotating ZAMO's, and the vacuum state smoothly interpolates between the “in” and “out” Boulware vacua.     

Slow rotation of compressible viscous fluid in cosmological universe

New analytic solutions for rotational perturbations of the Robertson-Walker metric are found in order to incorporate the possibility of a rotating viscous universe. The field equations impose restrictions on the matter rotationω(r, t), and some of the solutions for Ω(r, t) which is related to the local dragging of inertial frames are studied. In all the cases the rotational velocity is found to decay with increase of time. Geodesics of the metric are studied to reveal the intrinsic nature of rotation and to elucidate the role of Ω.     

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E in a given reference frame were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We show that a tetrad field contains two informations about local rotation, which usually do not coincide. We compute the energy operator in the inertial and the rotating frame, using three different tetrad fields. We find that Mashhoon’s term is there if the spatial triad rotates as does the reference frame—but then it is also there in the energy operator for the inertial frame. In fact, if one uses the same given tetrad field, the Dirac Hamiltonian operators in two reference frames in relative rotation differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.     

Energy and spatial momentum of charged rotating frames in tetrad gravity

We compute the total energy and the spatial momentum of four charged rotating (Kerr-Newman) frames by using the gravitational energy-momentum 3-form within the framework of the tetrad formulation of the general relativity theory. We show how the effect of the inertial always makes the total energy divergent. We use a natural regularization method, which yields the physical value for the total energy of the system. We show how the regularization method works on a number of different rotating frames that are related to each other by the local Lorentz transformation. We also show that the inertial has no effect on the spatial momentum components.     

Frame Dragging and Lense-Thirring Effect

We first describe some phenomena due to spin and mass-energy currents on clocks and photons, in particular we derive the delay in the travel time of photons due to the spin of a body both inside a rotating shell and outside a rotating body. We then review the 1995–2001 measurements of the gravitomagnetic field of Earth and Lense-Thirring effect obtained by analyzing the orbits of the two laser-ranged satellites LAGEOS (LAser GEOdynamics Satellite) and LAGEOS II. Finally, we report the latest measurement of the Lense-Thirring effect, obtained in 2003 with the two LAGEOS satellites over more than 10 years of data. This 2003 result fully confirms and improves our previous measurements of the Earth frame-dragging: the Lense-Thirring effect exists and its experimental value is within ~20% of what is predicted by Einstein's theory of general relativity.     

Horizonless,singularity-free,compact shells satisfying NEC

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose’s singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity.