On Schwarzschild's Topology in Brane-Worlds

TL;DR

This paper explores the topological structure of Schwarzschild space-time within brane-world models, revealing that its evolution involves a signature change in the bulk based on embedding and topology comparisons.

Contribution

It introduces a novel analysis of Schwarzschild topology in brane-worlds, linking geometric evolution to bulk signature change through embedding coordinate methods.

Findings

Topological differences influence the evolution of Schwarzschild space-time in brane-worlds.

Signature change in the bulk is necessary during the evolution of the brane-world.

Embedding coordinates reveal the relationship between different geometric states.

Abstract

The topological structure of Schwarzschild's space-time and its maximal analytic extension are investigated in context of brane-worlds. Using the embedding coordinates, these geometries are seen as different states of the evolution of a single brane-world. Comparing the topologies and the embeddings it is shown that this evolution must be followed by a signature change in the bulk.