Topology of Black Holes’ Horizons

Arturo Tozzi (Center for Nonlinear Science, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017,)
James F Peters (Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, Winnipeg, MB R3T 5V6,)

Emerging Science Journal
Vol 3, No 2 (2019): April

The Möbius strip spacetime topology and the entangled antipodal points on black hole surfaces, recently described by ‘t Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem from algebraic topology.  Considering this observation and other recent claims which suggest that quantum entanglement takes place on the antipodal points of a S3 hypersphere, a novel topological framework can be developed: a feature encompassed in an S2 unentangled state gives rise, when projected one dimension higher, to two entangled particles.  This allows us to achieve a mathematical description of the holographic principle occurring in S2.  Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.