Sagnac Effect, Ring Lasers and Terrestrial Tests of Gravity

Light can be used as a probe to explore the structure of space-time: this is usual in astrophysical and cosmological tests, however it has been recently suggested that this can be done also in terrestrial laboratories. Namely, the GINGER project aims at measuring post-Newtonian effects, such as the gravito-magnetic ones, in an Earth based laboratory, by means of a ring lasers array. Here, we first review the theoretical foundations of the Sagnac Effect, on which ring lasers are based, and then we study the Sagnac Effect in a terrestrial laboratory, emphasizing the origin of the gravitational contributions that GINGER aims at measuring. Moreover, we show that accurate measurements allow to set constraints on theories of gravity different from General Relativity. Eventually, we describe the experimental setup of GINGER.Comment: 24 pages, 1 figure; accepted for publication in Galaxies, Special Issue "Advances in Gravitational Research

Gravitomagnetic Field of Rotating Rings

In the framework of the so-called gravitoelectromagnetic formalism, according to which the equations of the gravitational field can be written in analogy with classical electromagnetism, we study the gravitomagnetic field of a rotating ring, orbiting around a central body. We calculate the gravitomagnetic component of the field, both in the intermediate zone between the ring and the central body, and far away from the ring and central body. We evaluate the impact of the gravitomagnetic field on the motion of test particles and, as an application, we study the possibility of using these results, together with the Solar System ephemeris, to infer information on the spin of ring-like structures.Comment: 8 pages, 2 figures; revised to match the version accepted for publication in Astrophysics and Space Scienc

Gravito-electromagnetic Aharonov-Bohm effect: some rotation effects revised

By means of the description of the standard relative dynamics in terms of gravito-electromagnetic fields, in the context of natural splitting, we formally introduce the gravito-magnetic Aharonov-Bohm effect. Then, we interpret the Sagnac effect as a gravito-magnetic Aharonov-Bohm effect and we exploit this formalism for studying the General Relativistic corrections to the Sagnac effect in stationary and axially symmetric geometries.Comment: 19 pages, 2 figures, in in Proceedings of Analysis, Manifolds and Geometric Structures in Physics, International Conference in Honour of Y. Choquet-Bruhat, June 2004, Isola d'Elba, Ital

Gravito-electromagnetic Effects of Massive Rings

The Einstein field equations in linear post-Newtonian approximation can be written in analogy with electromagnetism, in the so-called gravito-electromagnetic formalism. We use this analogy to study the gravitational field of a massive ring: in particular, we consider a continuous mass distribution on Keplerian orbit around a central body, and we work out the gravitational field generated by this mass distribution in the intermediate zone between the central body and the ring, focusing on the gravito-magnetic component that originates from the rotation of the ring. In doing so, we generalize and complement some previous results that focused on the purely Newtonian effects of the ring (thus neglecting its rotation) or that were applied to the case of rotating spherical shells. Eventually, we study in some simple cases the effect of the the rotation of the ring, and suggest that, in principle, this approach could be used to infer information about the angular momentum of the ring.Comment: 13 pages, LaTeX, revised to match the version accepted for publication in the International Journal of Modern Physics

Using Ring Laser Systems to Measure Gravitomagnetic Effects on Earth

Gravitomagnetic effects originates from the rotation of the source of the gravitational field and from the rotational features of the observers' frame. In recent years, gravitomagnetism has been tested by means of its impact on the precession of LAGEOS orbits and on the precession of spherical gyroscopes in the GP-B experiment. What we suggest here is that light can be used as a probe to test gravitomagnetic effects in an terrestrial laboratory: the proposed detector consists of large ring-lasers arranged along three orthogonal axes.Comment: 3 pages, in "QSO astrophysics, fundamental physics, and astrometric cosmology in the Gaia era" Porto-Portugal, June 6-9, 2011, Editors: S. Anton, M. Crosta, M.G. Lattanzi and A. Andrei. Memorie della Societ\`a Astronomica Italiana, Vol. 83 (2012

Light bending in f(T)f(T) gravity

In the framework of $f(T)$ gravity, we focus on a weak-field and spherically symmetric solution for the Lagrangian $f(T)=T+\alpha T^{2}$, where $\alpha$ is a small constant which parameterizes the departure from General Relativity. In particular, we study the propagation of light and obtain the correction to the general relativistic bending angle. Moreover, we discuss the impact of this correction on some gravitational lensing observables, and evaluate the possibility of constraining the theory parameter $\alpha$ by means of observations. In particular, on taking into account the astrometric accuracy in the Solar System, we obtain that $|\alpha| \leq 1.85 \times 10^{5}\, \mathrm{m^{2}}$; this bound is looser than those deriving from the analysis of Solar System dynamics, e.g. $|\alpha| \leq 5 \times 10^{-1}\, \mathrm{m^{2}}$, $|\alpha| \leq 1.8 \times 10^{4}\, \mathrm{m^{2}}$ or $|\alpha| \leq 1.2 \times 10^{2}\, \mathrm{m^{2}}$ . However we suggest that, since the effect only depends on the impact parameter, better constraints could be obtained by studying light bending from planetary objects.Comment: 14 pages, 1 figure; revised to match the version accepted for publication in IJMP

Rotation Effects and The Gravito-Magnetic Approach

Gravito-electromagnetism is somewhat ubiquitous in relativity. In fact, there are many situations where the effects of gravitation can be described by formally introducing "gravito-electric" and "gravito-magnetic" fields, starting from the corresponding potentials, in analogy with the electromagnetic theory (see also A. Tartaglia's contribution to these proceedings). The "many faces of gravito-electromagnetism" are related to rotation effects in both approximated and full theory approaches. Here we show that, by using a 1+3 splitting, relativistic dynamics can be described in terms of gravito-electromagnetic (GEM) fields in full theory. On the basis of this formalism, we introduce a "gravito-magnetic Aharonov-Bohm effect", which allows to interpret some rotation effects as gravito-magnetic effects. Finally, we suggest a way for measuring the angular momentum of celestial bodies by studying the gravito-magnetic effects on the propagation of electromagnetic signals.Comment: 3 pages, LaTeX, 1 EPS figure; to appear in the Proceedings for the ``XVI SIGRAV Conference'' in Vietri sul Mare (SA) 13-16 September 2004, References Changed, Misprints Correcte

Test of gravitomagnetism with satellites around the Earth

We focus on the possibility of measuring the gravitomagnetic effects due to the rotation of the Earth, by means of a space-based experiment that exploits satellites in geostationary orbits. Due to the rotation of the Earth, there is an asymmetry in the propagation of electromagnetic signals in opposite directions along a closed path around the Earth. We work out the delays between the two counter-propagating beams for a simple configuration, and suggest that accurate time measurements could allow, in principle, to detect the gravitomagnetic effect of the EarthComment: 6 pages, 3 figures; revised to match the version accepted for publication in EPJ

Weak-Field Spherically Symmetric Solutions in f(T)f(T) gravity

We study weak-field solutions having spherical symmetry in $f(T)$ gravity; to this end, we solve the field equations for a non diagonal tetrad, starting from Lagrangian in the form $f(T)=T+\alpha T^{n}$, where $\alpha$ is a small constant, parameterizing the departure of the theory from GR. We show that the classical spherically symmetric solutions of GR, i.e. the Schwarzschild and Schwarzschild-de Sitter solutions, are perturbed by terms in the form $\propto r^{2-2n}$ and discuss the impact of these perturbations in observational tests.Comment: 11 pages, LaTeX; revised to match the version accepted for publication in Physical Review

Lorentz contraction and accelerated systems

The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising when the world lines correspond to physically connected or disconnected objects. In all cases the special theory of relativity proves to be completely self-consistentComment: 7 pages, LaTeX, to be published in European Journal of Physic