TITLE:
Traversable Wormholes and the Brouwer Fixed-Point Theorem
AUTHORS:
Peter K. F. Kuhfittig
KEYWORDS:
Traversable Wormholes, Brouwer Fixed-Point Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.7,
July
9,
2020
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 x0 such that f(x0) = x0. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., b(r0) = r0 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.