Some Problems of Topology Change Description in the Theory of Space-Time

TL;DR

This paper examines the challenges of describing topology change in space-time within gravitation theory, highlighting limitations in four-dimensional models and proposing multidimensional theories as a potential framework for dynamical topology description.

Contribution

It clarifies the limitations of 4D theories for topology change and advocates for multidimensional models to enable dynamical descriptions of space-time topology.

Findings

Topology change in 4D theories is non-dynamical.

Multidimensional theories allow for dynamical topology changes.

Standard 4D models treat topology as boundary conditions.

Abstract

The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or constraints). Therefore, the possible changes of space topology in (3+1)-dimensions do not admit dynamical description nor in classical nor in quantum theories and the statements about dynamical supressing of topology change have no sence. In the framework of multidimensional theories the space (and space-time) may be considered as the embedded manifolds. It give the real posibilities for the dynamical description of the topology of space or space-time.