Angelo Tartaglia

We discuss the idea of a measurement that, making use of data from space interferometers, could detect the gravito-magnetic field generated by the rotation of the Milky Way, including the possible contribution of the dark matter halo. The galactic signal would be superposed to the gravito-magnetic field of the Sun. The proposed technique is based on the asymmetric propagation of light along the closed contour of the space interferometer, in a Sagnac-like approach. We discuss the principles of detection as well as some practical aspects of the proposed experiment using, as a case study, LISA, the most mature project to date. Both gravito-magnetic signals will be modulated thanks to the annual oscillation of the plane of the interferometer with respect to the galactic plane and to the spin axis of the Sun. Although larger than the detector intrinsic noise, these signals will be superposed to a much larger kinematic modulation due to orbital motion, making them very hard to be observed. We also mention a second phenomenon, where the gravito-magnetic field rotates the polarization of the propagating electromagnetic beams: the effect will be present in LISA, although exceedingly small and out of reach of present technology.

We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on emission coordinates in flat spacetime: in this case, we show that these coordinates can be defined using an approach based on simple geometrical properties of geodesic triangles. We analyse the 2-dimensional case and then we show how the whole procedure can be applied to 4 dimensions, also in terms of ordinary three-dimensional spheres. An analytic solution for the coordinates of the receiver is obtained. The solution remains valid at almost any place, in particular when redundancy in the number of emitters can be exploited.

We propose to locate transponders and atomic clocks in at least three of the Lagrange points of the Sun-Earth pair, with the aim of exploiting the time of flight asymmetry between electromagnetic signals travelling in opposite directions along polygonal loops having the Lagrange points at their vertices. The asymmetry is due to the presence of a gravito-magnetic field partly caused by the angular momentum of the Sun, partly originating from the angular momentum of the galactic dark halo in which the Milky Way is embedded. We list also various opportunities which could be associated with the main objective of this Lagrange Dark Halo Detector (LaDaHaD).

In this paper, we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr–Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton’s constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.

Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the framework of Newtonian gravity. The exact relativistic treatment of the problem is not an easy task, but this paper develops an approximate calculational scheme which computes for the first time the tiny effective-gravity correction to the equation of the surface for all points of which it is equally advantageous to regard the heliocentric motion as being perturbed by the attraction of Jupiter, or the jovicentric motion as being perturbed by the attraction of the Sun. This analysis completes the previous theoretical investigations of effective-gravity corrections to the Newtonian analysis of three-body systems, and represents an intermediate step towards relativistic effects on cometary motions.

The paper concerns the use of satellites of the Galileo constellation for relativistic positioning and for measurements of the gravito-magnetic effects induced by the angular momentum both of the Earth and of the dark halo of the Milky Way. The experimental approach is based on the generalized Sagnac effect, induced both by the rotation of the device and the fact that the observer is located within the gravitational field of a spinning mass. Among the possible sources there is also the angular momentum of the dark halo of the Milky Way. Time modulation of the expected signal would facilitate its disentanglement from the other contributions. The modulation could be obtained using satellites located on different orbital planes.

Energy communities are associations of producers and consumers of energy set up to reduce the dependence on fossil fuels and optimise the use of energy for the advantage of the members. This paper presents an experiment being implemented in the territory around the town of Pinerolo in western Piedmont. Encouraging results are reported.