Embeddings and time evolution of the Schwarzschild wormhole

TL;DR

This paper demonstrates how to embed spacelike slices of the Schwarzschild wormhole in three-dimensional space, providing visualizations of its dynamic evolution and the 'pinching off' process at specific Kruskal times.

Contribution

It introduces a method to embed Schwarzschild wormhole slices in R3 and visualizes their evolution over Kruskal time, including the nontraversable 'pinching off' behavior.

Findings

Successful embedding of Schwarzschild wormhole slices in R3.

Visualizations of wormhole dynamics at various Kruskal times.

Illustration of the 'pinching off' process at critical times.

Abstract

We show how to embed spacelike slices of the Schwarzschild wormhole (or Einstein-Rosen bridge) in R3. Graphical images of embeddings are given, including depictions of the dynamics of this nontraversable wormhole at constant Kruskal times up to, and beyond, the "pinching off" at Kruskal times \pm1.