The case for the Universe to be a quantum black hole

We present a necessary and sufficient condition for an object of any mass m to be a quantum black hole (q.b.h.): “The product of the cosmological constant Λ and the Planck’s constantℏ, Λ and ℏcorresponding to the scale defined by this q.b.h., must be of order one in a certain universal system of units”. In this system the numerical values known for Λ are of order one in cosmology and about 10122 for Planck’s scale. Proving that in this system the value of the cosmological ℏc is of order one, while the value of ℏ for the Planck’s scale is about 10−122, both scales satisfy the condition to be a q.b.h., i.e. Λℏ≈1. In this sense the Universe is a q.b.h. We suggest that these objects, being q.b.h.’s, give us the linkage between thermodynamics, quantum mechanics, electromagnetism and general relativity, at least for the scale of a closed Universe and for the Planck’s scale. A mathematical transformation may refer these scales as corresponding to infinity (our universe) and zero (Planck’s universe), in a “scale relativity” sense.