Covariance and meaning

TL;DR

This paper explores how additional factors beyond local geometry influence the interpretation of space-time models, introducing a new time-dependent spherically symmetric model that could serve as a local perturbation or alternative to asymptotic Minkowskian assumptions.

Contribution

It presents a novel time-dependent, locally-Minkowskian spherically symmetric space-time model with constant-force test particles, expanding the understanding of space-time meaning beyond intrinsic geometry.

Findings

The model describes a globally unrealistic but potentially useful local perturbation.

It offers an alternative to asymptotic Minkowskian assumptions for gravitational fields.

The model demonstrates how additional factors influence space-time interpretation.

Abstract

Several other factors, besides the intrinsic local geometry, contribute to give a meaning to a space-time model. The simplest example comes from comparing Minkowski's and Milne's model, that both have a null Riemann tensor. We add to these two models a third one which describes a time-dependent locally-Minkowskian spherically symmetric space-time on which every test-particle at rest with respect to the center of symmetry sustains a constant force. Although the model is globally grossly un-realistic we think that it can be helpful to describe a local perturbation of an homogeneous cosmological model. Or as a substitute to the very far away asymptotic Minkowskian behavior usually assumed to describe the gravitational field of compact spherical bodies.