443 research outputs found

### 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

### 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

### 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

### Slowly rotating voids in cosmology

We consider a spacetime consisting of an empty void separated from an almost
Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) dust universe by a spherically
symmetric, slowly rotating shell which is comoving with the cosmic dust. We
treat in a unified manner all types of the FLRW universes. The metric is
expressed in terms of a constant characterizing the angular momentum of the
shell, and parametrized by the comoving radius of the shell. Treating the
rotation as a first order perturbation, we compute the dragging of inertial
frames as well as the apparent motion of distant stars within the void.
Finally, we discuss, in terms of in principle measurable quantities, 'Machian'
features of the model.Comment: 21 pages, 5 figures, REVTex, accepted for publication in
Class.Quant.Gravit

### Information-Disturbance Theorem for Mutually Unbiased Observables

We derive a novel version of information-disturbance theorems for mutually
unbiased observables. We show that the information gain by Eve inevitably makes
the outcomes by Bob in the conjugate basis not only erroneous but random

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