Gravitational Field of a Spinning Cosmic String

We study the effect of internal space rotation on the gravitational properties of infinite straight and stationary cosmic string. From the approximate solution of Einsten equations for the spinning Q-lump string we obtain long range gravitational accelleration resembling that of a rotating massive cylindrical shell. We also compute the angular velocity of the inertial frame dragging and the angle of light deflection by the Q-lump string. Matter accretion on to spinning strings can play a role in galaxy formation when the angular velocity times the string width is comparable to the speed of light.Comment: 14 page

MEASURING GRAVITOMAGNETIC EFFECTS BY MEANS OF RING LASERS

Light is a good probe for general relativistic effects. Exploiting the asymmetry of the propagation in the vicinity of a central rotating mass it is possible to use a ring laser in order to measure the frame dragging of the reference frames by the gravitational field of the Earth (Lense-Thirring effect). I shall present the G-GranSasso experiment whose objective is precisely to measure the Lense-Thirring and the de Sitter effects in a terrestrial laboratory. The experimental apparatus will be made of a set of at least three, differently oriented, ring lasers rigidly attached to a central "monument". The signal will be in the form of the beat frequency produced in the annular cavity of each laser by the rotational anisotropy. The laboratory will be located underground in the Laboratori Nazionali del Gran Sasso facility, in Italy. The required sensitivity is just one order of magnitude below the performance of the best existing instruments and the new design will attain i

Validity and failure of some entropy inequalities for CAR systems

Basic properties of von Neumann entropy such as the triangle inequality and what we call MONO-SSA are studied for CAR systems. We show that both inequalities hold for any even state. We construct a certain class of noneven states giving counter examples of those inequalities. It is not always possible to extend a set of prepared states on disjoint regions to some joint state on the whole region for CAR systems. However, for every even state, we have its `symmetric purification' by which the validity of those inequalities is shown. Some (realized) noneven states have peculiar state correlations among subsystems and induce the failure of those inequalities.Comment: 14 pages, latex, to appear in JMP. Some typos are correcte

Post-Newtonian Approximation in Maxwell-Like Form

The equations of the linearized first post-Newtonian approximation to general relativity are often written in "gravitoelectromagnetic" Maxwell-like form, since that facilitates physical intuition. Damour, Soffel and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlinearities, in Maxwell-like form. This paper summarizes that DSX Maxwell-like formalism (which is not easily extracted from their celestial mechanics papers), and then extends it to include the post-Newtonian (Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e. gravitational stress tensor) and law of momentum conservation in Maxwell-like form. The authors and their colleagues have found these Maxwell-like momentum tools useful for developing physical intuition into numerical-relativity simulations of compact binaries with spin.Comment: v4: Revised for resubmission to Phys Rev D, 6 pages. v3: Reformulated in terms of DSX papers. Submitted to Phys Rev D, 6 pages. v2: Added references. Changed definitions & convention

Beyond Gravitoelectromagnetism: Critical Speed in Gravitational Motion

A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity is due to the existence of a critical speed. Dynamics of particles moving faster than the critical speed could then be contrary to Newtonian expectations. Working within the framework of gravitoelectromagnetism, the implications of the existence of a critical speed are explored. The results are expected to be significant for high energy astrophysics.Comment: 13 pages, to appear in the Special December 2005 Issue of Int. J. Mod. Phys.

Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors

One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss an analogue of such a magnetoelectric effect in the thermal (or gravitational) and the magnetic dipole responses in all symmetry classes which admit topologically non-trivial insulators or superconductors to exist in three dimensions. In particular, for topological superconductors (or superfluids) with time-reversal symmetry which lack SU(2) spin rotation symmetry (e.g. due to spin-orbit interactions), such as the B phase of $^3$He, the thermal response is the only probe which can detect the non-trivial topological character through transport. We show that, for such topological superconductors, applying a temperature gradient produces a thermal- (or mass-) surface current perpendicular to the thermal gradient. Such charge, thermal, or magnetic dipole responses provide a definition of topological insulators and superconductors beyond the single-particle picture. Moreover we find, for a significant part of the 'ten-fold' list of topological insulators found in previous work in the absence of interactions, that in general dimensions the effective field theory describing the space-time responses is governed by a field theory anomaly. Since anomalies are known to be insensitive to whether the underlying fermions are interacting or not, this shows that the classification of these topological insulators is robust to adiabatic deformations by interparticle interactions in general dimensionality. In particular, this applies to symmetry classes DIII, CI, and AIII in three spatial dimensions, and to symmetry classes D and C in two spatial dimensions.Comment: 16 pages, 2 figure

Black string and velocity frame dragging

We investigate velocity frame dragging with the boosted Schwarzschild black string solution and the boosted Kaluza-Klein bubble solution, in which a translational symmetry along the boosted $z$-coordinate is implemented. The velocity frame dragging effect can be nullified by the motion of an observer using the boost symmetry along the $z-$coordinate if it is not compact. However, in spacetime with the compact $z-$coordinate, we show that the effect cannot be removed since the compactification breaks the global Lorentz boost symmetry. As a result, the comoving velocity is dependent on $r$ and the momentum parameter along the $z-$coordinate becomes an observer independent characteristic quantity of the black string and bubble solutions. The dragging induces a spherical ergo-region around the black string.Comment: 8 pages, no figure, some correction

Spin Dynamics of the LAGEOS Satellite in Support of a Measurement of the Earth's Gravitomagnetism

LAGEOS is an accurately-tracked, dense spherical satellite covered with 426 retroreflectors. The tracking accuracy is such as to yield a medium term (years to decades) inertial reference frame determined via relatively inexpensive observations. This frame is used as an adjunct to the more difficult and data intensive VLBI absolute frame measurements. There is a substantial secular precession of the satellite's line of nodes consistent with the classical, Newtonian precession due to the non-sphericity of the earth. Ciufolini has suggested the launch of an identical satellite (LAGEOS-3) into an orbit supplementary to that of LAGEOS-1: LAGEOS-3 would then experience an equal and opposite classical precession to that of LAGEOS-1. Besides providing a more accurate real-time measurement of the earth's length of day and polar wobble, this paired-satellite experiment would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite, and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. Consequently, we undertake here a theoretical effort to model the spin ndynamics of LAGEOS. In this paper we present our preliminary results.Comment: 16 pages, RevTeX, LA-UR-94-1289. (Part I of II, postscript figures in Part II

Cosmological gravitomagnetism and Mach's principle

The spin axes of gyroscopes experimentally define local non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? We consider linear perturbations of Friedmann-Robertson-Walker cosmologies with k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin axes of gyroscopes relative to the directions of geodesics to quasars in the asymptotic unperturbed FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of linear cosmological gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state for cosmological matter, are: 1) The dragging of a gyroscope axis by rotational perturbations of matter beyond the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot is the derivative with respect to cosmic time. 2) If the perturbation of matter is a homogeneous rotation inside some radius around a gyroscope, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For the most general linear cosmological perturbations the time-evolution of all gyroscope spin axes exactly follow a weighted average of the energy currents of cosmological matter. The weight function is the same as in Ampere's law except that the inverse square law is replaced by the Yukawa force with the Hubble-dot cutoff. Our results demonstrate (in first order perturbation theory for FRW cosmologies with k = 0) the validity of Mach's hypothesis that axes of local non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde

Celestial mechanics in Kerr spacetime

The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by solving the Hamilton-Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with the radial, polar and azimuthal components of orbital motion. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this article, it is shown that the fundamental frequencies are geometric invariants and explicit formulas in terms of quadratures are derived. The numerical evaluation of these formulas in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or the inclination parameter $\theta_{-}$ are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulas.Comment: 25 pages (LaTeX), 5 figures, submitted to Class. Quantum Gra