On a Possibility of Phase Transitions in the Geometric Structure of   Space-Time
  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. 
G.Yu. Bogoslovsky, H.F. Goenner