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The Sagnac effect is usually considered as being a relativistic effect produced in an interferometer when the device is rotating. General relativistic explanations are known and already widely explained in many papers. Such general relativistic approaches are founded on Einstein's equivalence principle (EEP), which states the equivalence between the gravitational "force" and the pseudo-force experienced by an observer in a non-inertial frame of reference, included a rotating observer. Typically, the authors consider the so-called Langevin-Landau-Lifschitz metric and the path of light is determined by null geodesics. This approach partially hides the physical meaning of the effect. It seems indeed that the light speed varies by c ± ωr in one or the other direction around the disk. In this paper, a slightly different general relativistic approach will be used.The different "gravitational field" acting on the beam splitter and on the two rays of light is analyzed. This different approach permits a better understanding of the physical meaning of the Sagnac effect.

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In this paper, we modify the geometry of Rindler space so as to include an upper limit on the acceleration. Caianiello and his collaborators, in a series of papers, have analyzed the corrections to the classical spacetime metrics due to the existence of a maximal acceleration. Our goal is to derive, in this context, in a very simple way, the so-called Unruh temperature.

Einstein's gravitational theory gave rise to a new conception of the Universe and Cosmology has been enclosed in the realm of Science and not only of Philosophy as before the Einstein work. Despite this, the presence of the Big Bang singularity, flatness and horizon problems led to the statement that Standard Cosmological Model, based on General Relativity and Standard Model of particle physics, is inadequate to describe the Universe in extreme regimes. Due to this facts, alternative gravitational theories and alternative approaches to cosmology have been proposed during the years. One of the most fruitful approach has been that of Projective Relativity and, in this paper, we analyze the developments of this theory. Projective Relativity, initially proposed by Fantappié and subsequently developed by Arcidiacono, has been recently revisited by prof. Ignazio Licata and other authors. The cosmological consequences of such extension appear relevant. In the following, we analyze the effects of the group approach on the metrics and on the dynamics and we will consider its properties in connection with varying speed of light.

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We want to shed light on some discussed aspects of the principle of equivalence. We consider two different phases in the evolution of the principle. We pay attention to the fact that some textbooks do not dwell on the mathematical meaning of ‘locally flat spacetime’, which can confuse students and, occasionally, can also lead to misinterpretations. For example, the non-eliminability of tidal forces, not even locally, may suggest that the equivalence principle is wrong. By contrast, we want to show that this is in perfect agreement with the Einstein geometrical interpretation of spacetime. Finally, in order to check the approximations used in the Gedankenexperiment of an elevator, we estimate explicitly the magnitude of the deflection of light and the effects of tidal forces in a ‘real lift’.

Starting from the origin of Einstein general relativity (GR) the request of Mach on the theory's structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of Equivalence Principle (EP). The MOND theory by Milgrom proposes a modification of Newtonian dynamics and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a non geodesic ratio mi/mg can be fixed and that Milgrom acceleration is retrieved at low energies.