On a Possibility of Phase Transitions in the Geometric Structure of Space-Time

TL;DR

This paper explores the potential for phase transitions in the geometric structure of space-time, suggesting it can switch between Riemann and Finsler geometries, affecting its manifold dynamics.

Contribution

It introduces the concept of phase transitions between different geometric states of space-time, expanding the understanding of its possible metric configurations.

Findings

Space-time can exist in states described by Riemann or Finsler geometry.

Transitions between these states are analogous to phase transitions.

These transitions influence the evolution of space-time manifold.

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.