Geometrical Structures of Space-Time in General Relativity

TL;DR

This paper provides a unified framework for understanding various geometrical structures of space-time in general relativity, clarifying their relationships and physical significance.

Contribution

It introduces a standard criterion of naturalness to unify and relate different geometrical structures of space-time in a comprehensive manner.

Findings

Unified description of conformal, volume, projective, and linear connection structures

Relationships established among different geometrical structures

Clarification of the physical meaning of geometric magnitudes

Abstract

Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep understanding of them has consequences on the dynamical role played by geometry. We present a unified description of those geometrical structures, with a standard criterion of naturalness, and then we establish relationships among them and try to clarify the meaning of associated geometric magnitudes.