Traversable wormholes and the Brouwer fixed-point theorem

TL;DR

This paper explores the mathematical connection between the Brouwer fixed-point theorem and the existence of traversable wormholes, suggesting that fixed points in topology can imply physical wormhole structures.

Contribution

It establishes a novel link between topological fixed-point theorems and the theoretical existence of traversable wormholes in physics.

Findings

Fixed points correspond to wormhole throats under certain conditions

Mathematical topology can imply physical structures without new physical assumptions

The existence of wormholes can be deduced from pure mathematical theorems

Abstract

The Brouwer fixed-point theorem in topology states that for any continuous mapping $f$ on a compact convex set into itself admits a fixed point, i.e., a point $x_0$ such that $f(x_0)=x_0$. Under certain conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., $b(r_0)=r_0$ for the shape function $b=b(r)$. The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.