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arXiv · 2007.05486

Traversable wormholes and the Brouwer fixed-point theorem

Peter K. F. Kuhfittig
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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.

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Peter K. F. Kuhfittig. 2021-09-25. Traversable wormholes and the Brouwer fixed-point theorem. https://doi.org/10.4236/jamp.2020.87096

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