“Now there’s a look in your eyes, Like black holes in the sky.”
Black Hole physics is the other ﬁeld where the clash between the quantum and the classical appears. Although there is universal agreement that General Relativity will be modiﬁed so that the Black Hole singularities be resolved, the idea that new physics at the scale of the horizon is usually dismissed. The argument commonly used is that the potential of the gravitational ﬁeld at the horizon of the Black Hole scales as ∝ 1/M and thus for macroscopic objects (large M) quantum phenomena are not relevant. However the latter is at least misleading given that it is well known that the phenomenon of quantum coherence does not necessarily require strong ﬁelds (we claim that is happening in our brain19). The existence of the horizon in combination with the quantum theory would give rise to Hawking radiation which is thermal and at the process of Black Hole evaporation leading to the Black Hole Information Paradox. In the absence of any experimental result indicating Hawking radiation20 we think that is not very wise to give away one the most fundamental principles of quantum theory: Unitarity in favour of an ambiguous extrapolation beyond the classical horizon of the Classical Theory of General Relativity.
Given that horizons21 give rise only to problems, we consider them unnatural. Inspired by our model of consciousness, we believe that is much more reasonable to assume that a phase transition is taking place at the scale of the horizon of the black hole. The interior is a quantum condensate. Given that all known matter is fermionic we will assume that black holes are fermionic quantum condensates (although we have no evidence whatsoever or that22) . A spin 1/2 fermionic condensate has a SU(2) symmetry associated with it. Note that in the presence of preferred axis the latter is reduced to a Z2 symmetry. At the phase transition the breaking of this symmetry can be spontaneous or explicit. The presence of strong magnetic ﬁeld in the astrophysical black hole candidates suggest explicit breaking. As a result, the quantum character of the condensate is suppressed given that a single vacuum is strongly preferred. As in the case of brain function there is no information loss paradox. Given that the interior of the black hole is a coherent state, its entropy will come from its boundary where the quantum condensate is expected to start forming. Given the latter picture the area law for the black hole entropy comes as no surprise. However if this is the case it is hard to believe in an exact coefficient (e.g. the expected 1/4) for the area law of the black hole entropy unless additional symmetries are imposed.
All the previous, of course, must be addressed in the context of a theory that provides a consistent theory of quantum gravity. In the context of String Theory something similar to a phase transition occurs when the Calabi-Yau shape goes through a space-tearing conifold transition. But also, in the context of Loop Quantum Gravity the Black Hole Entropy can be done approximately using Spin Networks and for large enough cases does give the area law
20 A result based on ad-hoc boundary conditions on the horizon of the Black Hole giving rise to negative speciﬁc heat for the Black Hole.
21 Note that similar arguments apply for the Cosmological Horizons: e.g. in the case of Schwarzschild-de Sitter Black Hole solution the two horizons (Black Hole – Cosmological) can be interchanged by appropriate change of coordinates.
22 However note: In the solution for Kerr-Neuman Black Hole the Gyromagnetic Ratio is 2 (Mass) ∗(MagneticMoment)/ (Charge) ∗(AngularMomentum) = 2 just like in the case of the electron.