An Approximated Solution of the Einstein Equations for a Rotating Body with Negligible Mass

The paper considers the problem of finding the metric of space time around a rotating, weakly gravitating body. Both external and internal metric tensors are consistently found, together with an appropriate source tensor. All tensors are calculated at the lowest meaningful approximation in a power series. The two physical parameters entering the equations (the mass and the angular momentum per unit mass) are assumed to be such that the mass effects are negligible with respect to the rotation effects. A non zero Riemann tensor is obtained. The order of magnitude of the physical effects is discussed.     

On the Anistropy of the Speed of Light on a Rotating Platform

The paper discusses a recently posed paradox in relativity concerning the speed of light as measured by an observer on board a rotating turn-table. The counter-intuitive problem put forward by F. Selleri concerns the theoretical prediction of an anisotropy in the speed of light in a reference frame comoving with the edge of a rotatiing disc even in the limit of zero acceleration. The paradox not only challenges the internal consistency of the special relativity theory but also undermines the basic tenet of the conventionality of simultaneity thesis of relativity. The present paper resolves the issue in a novel way by recasting the original paradox in the Galilean world and thereby revealing, in a subtle way, the weak points of the reasonings leading to the fallacy. As a background the standard and the non-standard synchronies in the relativistic as well as in the Galilean world are discussed. In passing, this novel approach also clarifies (contrary to often made assertions in the literature) that the so-called desynchronization of clocks cannot be regarded as the root cause of the Sagnac effect. Finally in spite of the flaw in the reasonings leading to the paradox Selleri's observation regarding the superiority of the absolute synchrony over the standard one for a rotation observer has been upheld.     

Some Comments on a Recently Derived Approximated Solution of the Einstein Equations for a Spinning Body with Negligible Mass

Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both external and internal metric tensors have been consistently found, together an appropriate source tensor; moreover, it may suggest possible experimental checks since the conditions of validity of the considered metric are well satisfied at Earth laboratory scales. However, it should be pointed out that reasonable doubts exist if it is physically meaningful because it is not clear if the source tensor related to the adopted metric can be realized by any real extended body. Here we derive the geodesic equations of the metric and analyze the allowed motions in order to disclose possible unphysical features which may help in shedding further light on the real nature of such approximated solution of the Einstein equations.     

Exact Form Factors for the Josephson Tunneling Current and Relative Particle Number Fluctuations in a Model of Two Coupled Bose–Einstein Condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose–Einstein condensates. This is achieved by studying the exact solution of the model with in the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.