From the elasticity theory to cosmology and vice versa

The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe, including the accelerated expansion. The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold (i.e. in space-time) by the curvature, be it induced by the presence of a texture defect or by a matter/energy distribution. The additional term is sufficient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy. Then, we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces. Finally, it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.Comment: 11 pages, 3 figure

Angular momentum effects in weak gravitational fields

It is shown that, contrary to what is normally expected, it is possible to have angular momentum effects on the geometry of space time at the laboratory scale, much bigger than the purely Newtonian effects. This is due to the fact that the ratio between the angular momentum of a body and its mass, expressed as a length, is easily greater than the mass itself, again expressed as a length.Comment: LATEX, 8 page

Einstein-Cartan theory as a theory of defects in space-time

The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space-time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations.Comment: 18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal of Physics, revised version with typos correcte

Relativistic contraction and related effects in noninertial frames

Although there is no relative motion among different points on a rotating disc, each point belongs to a different noninertial frame. This fact, not recognized in previous approaches to the Ehrenfest paradox and related problems, is exploited to give a correct treatment of a rotating ring and a rotating disc. Tensile stresses are recovered, but, contrary to the prediction of the standard approach, it is found that an observer on the rim of the disc will see equal lengths of other differently moving objects as an inertial observer whose instantaneous position and velocity are equal to that of the observer on the rim. The rate of clocks at various positions, as seen by various observers, is also discussed. Some results are generalized for observers arbitrarily moving in a flat or a curved spacetime. The generally accepted formula for the space line element in a non-time-orthogonal frame is found inappropriate in some cases. Use of Fermi coordinates leads to the result that for any observer the velocity of light is isotropic and is equal to $c$, providing that it is measured by propagating a light beam in a small neighborhood of the observer.Comment: 15 pages, significantly revised version, title changed, to appear in Phys. Rev.

Interacting supernovae and supernova impostors. LSQ13zm: an outburst heralds the death of a massive star

We report photometric and spectroscopic observations of the optical transient LSQ13zm. Historical data reveal the presence of an eruptive episode (that we label as ‘2013a’) followed by a much brighter outburst (‘2013b’) three weeks later, that we argue to be the genuine supernova explosion. This sequence of events closely resemble those observed for SN 2010mc and (in 2012) SN 2009ip. The absolute magnitude reached by LSQ13zm during 2013a (M_R=−14.87±0.25mag) is comparable with those of supernova impostors, while that of the 2013b event (M_R=−18.46±0.21mag) is consistent with those of interacting supernovae. Our spectra reveal the presence of a dense and structured circumstellar medium, probably produced through numerous pre-supernova mass-loss events. In addition, we find evidence for high-velocity ejecta, with a fraction of gas expelled at more than 20000 km s^(−1). The spectra of LSQ13zm show remarkable similarity with those of well-studied core-collapse supernovae. From the analysis of the available photometric and spectroscopic data, we conclude that we first observed the last event of an eruptive sequence from a massive star, likely a Luminous Blue Variable, which a short time later exploded as a core-collapse supernova. The detailed analysis of archival images suggest that the host galaxy is a star-forming Blue Dwarf Compact Galaxy

Emission vs Fermi coordinates: applications to relativistic positioning systems

A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi triad, as described by the Fermi metric. In the case of a Schwarzschild spacetime modeling the gravitational field around the Earth and an observer at rest at a fixed spacetime point, these coordinates realize a relativistic positioning system alternative to the current GPS system. The latter is indeed essentially conceived as Newtonian, so that it necessarily needs taking into account at least the most important relativistic effects through Post-Newtonian corrections to work properly. Previous results concerning emission coordinates in flat spacetime are thus extended to this more general situation. Furthermore, the mapping between spacetime coordinates and emission coordinates is completely determined by means of the world function, which in the case of a Fermi metric can be explicitly obtained.Comment: 12 pages iop style, 2 eps figures, to appear on Classical and Quantum Gravity, 200