Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 3

Topological surgery in cosmic phenomena

Pages: 701 – 765

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n3.a3

Authors

Stathis Antoniou (Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece)

Louis H. Kauffman (Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, Il., U.S.A.; and Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia)

Sofia Lambropoulou (Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Greece)

Abstract

We connect topological changes that can occur in $3$-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena, including relationships between quantum entanglement and wormhole formation. By considering the initial manifold as the $3$-dimensional spatial section of spacetime, we describe the changes of topology occurring in these processes by determining the resulting $3$-manifold and its fundamental group. As these global changes are induced by local processes, we use the local form of Morse functions to provide an algebraic formulation of their temporal evolution and propose a potential energy function which, in some cases, could give rise to the local forces related to surgery. We further show how this topological perspective gives new insight for natural phenomena exhibiting surgery, in all dimensions, while emphasizing the $3$-dimensional case, which describes cosmic phenomena. This work makes new bridges between topology and natural sciences and creates a platform for exploring geometrical physics.

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Published 4 December 2019