The case for the Universe to be a quantum black hole

Original Article


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, Λ and 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 c is of order one, while the value of for the Planck’s scale is about 10−122, both scales satisfy the condition to be a q.b.h., i.e. Λ≈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.


Cosmology Quantum black holes Gravitational radius Compton wavelength Planck’s constant Boltzmann constant 


04.70.-s 97.60.Lf 98.80.Qc 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.E.U.I.T. AeronáuticaMadridSpain

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