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 constant ℏ, Λ and ℏ corresponding 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 ℏ _c 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.