Topological Assessment of Entangled Particles on Black Hole Horizons

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.