On the possibility of phase transitions in the geometric structure of space-time

Abstract

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase transitions in its geometric structure. These transitions together with the evolution of each of the possible metric states make up the general picture of space-time manifold dynamics. 95.30.Sf; 98.80.Bp; 98.80.Hw; According to the contemporary cosmological models [1], space-time is Riemannian, i.e. locally isotropic, and preserves its local isotropy in the process of the Universe evolution. At the same time there exist some indirect indications of the fact that nowadays spacetime has a weak relic local anisotropy and therefore it is not unlikely that it is described by Finsler geometry [2] rather than by Riemann geometry. Moreover, if it appears that the Hubble constant has no dipole anisotropy correlated with the dipole anisotropy of the microwave background radiation then it will unequivocally indicate a strong local anisotropy of space-time at the early stage of the Universe evolution. PACSOne of the possible mechanisms of the appearance of a local anisotropy in space-time is the induced phase transition in its geometric structure, caused by the breakdown of higher gauge symmetries and by the appearance of masses in fundamental fields of matter. This involves changes in the metric properties of space-time manifold and it goes over from a state described by Riemann geometry into a state described by Finsler geometry. Since Finslerian space-time differs from Riemannian space-time by the anisotropy of its tangent spaces, in such a transition there occurs a flagrant violation of the local Lorentz

Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy

“…As early as our works [19], where the entirely anisotropic Finslerian event space was first treated, Hubert Goenner and the author encountered the unusual situation in which the Einstein procedure of exchange of light signals failed to properly determine the magnitude of the observable 3-velocity and was only able to determine the components of the observable 3-velocity. As a result, the necessity arose that an algorithm be constructed to permit determination of the magnitude of the observable 3-velocity, thereby formalizing the condition that singles out the domain of causally-related events in space (8).…”

“…has been obtained in [19]. Three parameters (r 1 , r 2 and r 3 ) characterize the anisotropy of event space (8) and are restricted by the conditions…”

“…The first type Finslerian space is a space with partially broken 3D isotropy, while the second one exhibits an entirely broken 3D isotropy. Described below will be their basic properties (for more details see [8,19]). …”

“…To obtain restrictions on the permissible v i values, Hubert Goenner and me [19] made the valid assumption that motion of a particle is in correspondence with such events in space (8), for which not only the condition dx 0 > 0, but also the set of inequalities…”

“…Therefore, the Einstein procedure of exchange of light signals makes it possible to obtain only the respective sectorial components of observable 3-velocity (see [19])…”