Will the 't Hooft's black hole model be for quantum gravity what the Bohr's hydrogen atom was to quantum physics ?
Regarding black holes as quantum matter produces new results about the topology in space-time and its non-commutative nature.
In the following video the famous dutch physicist explains how three insights* could turn black holes from complete mysteries to quantum systems as transparent as the hydrogen atom...
* the first one is the gravitational interaction between in- and out-going particles, the second is a spherical wave expansion yielding uncoupled modes to describe transparently the mechanism by which black holes return the absorbed information to the outside world and the third one is an antipodal identification of points on the horizon that turns mixed states of Hawking particles into pure states. Interestingly his results imply new constraints on the topology and the boundary conditions of general coordinate transformations removing the firewall problem (that might have been more than an academic wall after all)!
Slides of this colloqium held at ENS are available here.
Under normal circumstances, the gravitational force between sub-atomic particles is so weak that these difficulties are insignificant, but at extremely tiny distance scales, of the order of 10⁻³³ cm, this force will become strong. We are tempted to believe that, at these tiny distance scales, the fabric of space and time is affected by quantum mechanical phenomena, but exactly how this happens is still very mysterious. One approach to this problem is to ask: under which circumstance is the gravitational force as strong as it ever can be? The answer to this is clear: at the horizon of a black hole
As I have been emphasizing for more than three decades now, the text book description of quantum gravity (where the Einstein-Hilbert action is quantized using standard procedures) shows flaws here that run deeper than that it generates infinities: it does not allow a description of a black hole as a single quantum object. This is a direct contradiction, a paradox, a problem shouting for a radical solution, saying that there is something we are not doing right. For a long time I was convinced that also superstring theory, in this respect is fundamentally faulty, but two developments forced me to be more cautious here. One: it is now possible to describe at least some members of the black hole family using string theory with multidimensional membranes, called D-branes, added to it. The objects thus obtained are purely quantum mechanical and agree with naive expectations so well that many of my colleagues are convinced that “string theory solves the problem”. But why does this happen? How does string theory resolve the paradox? Curiously, string theorists themselves do not quite understand this. I think that important improvements of the theory are necessary.
... I claim to have found how to put quantum gravity back in line so as to restore quantum mechanics for pure black holes. It does not happen automatically, you need a new symmetry. It is called local conformal invariance. This symmetry is often used in superstring and supergravity theories, but very often the symmetry is broken by what we call “anomalies”. These anomalies are often looked upon as a nuisance but a fact of life. I now claim that black holes only behave as required in a consistent theory if all conformal anomalies cancel out. This is a very restrictive condition, and, very surprisingly, this condition also affects the Standard Model itself. All particles are only allowed to interact with gravity and with each other in very special ways. Conformal symmetry must be an exact local symmetry, which is spontaneously broken by the vacuum, exactly like in the Higgs mechanism.
... What I should have discovered 30 years ago is that the algebraical relations for the black hole microstates can be solved much more explicitly by expanding everything in spherical harmonics. The result reveals something that came totally unexpected: the black hole evolution operator is only unitary if, on the black hole horizon, antipodal points are identified, so that, the area of the horizon is only half of what is usually written down! This affects space-time topology of the black hole metric. This actually had already been foreseen long ago by Whiting and Sanchez, so I have no priority claim here, but I don't think they saw the implications: black holes are not in a thermally mixed state, as was always claimed by Hawking, but they form pure, entangled states! Hawking particles emitted at one point of the black hole are 100% entangled with the particles emerging at the other side. This resolves important issues, such as the "firewall problem" ... But some problems remain: these microstates are not described as Standard Model states, while they should be. We have to figure out how this goes.
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