Topology of Black Holes' Horizons

Borsuk-Ulam Theorem Antipodal Points Quantum Entanglement Holographic Principle t'Hooft Möbius Strip.

Authors

  • Arturo Tozzi
    tozziarturo@libero.it
    Center for Nonlinear Science, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017,, United States
  • James F Peters Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6,, Canada

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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.