Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Topological Assessment of Entangled Particles on Black Hole Horizons

Version 1 : Received: 21 September 2018 / Approved: 22 September 2018 / Online: 22 September 2018 (23:29:55 CEST)

A peer-reviewed article of this Preprint also exists.


The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S3 hypersphere, a novel framework can be developed, based on algebraic topological issues: 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.


Borsuk-Ulam theorem; antipodal points; quantum entanglement; holographic principle


Physical Sciences, Quantum Science and Technology

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