A river model of space

TL;DR

This paper introduces a river model of space within general relativity, depicting space as a flowing medium that helps intuitively understand the behavior of light and particles near black hole and cosmological horizons.

Contribution

It presents a simple, intuitive model of physical space as a flowing river for Schwarzschild and de Sitter spacetimes, clarifying horizon phenomena.

Findings

Space flows radially in Schwarzschild spacetime towards the singularity.

Space flows outward in de Sitter spacetime towards infinity.

The model explains light and particle behavior at horizons intuitively.

Abstract

Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes.