Fun with entangled near-extremal black holes

Moyses has pointed out that I haven't discussed the July 2018 paper by Maldacena-Milekhin-Popov (Princeton) about a new wormhole solution. The wormhole is traversable. The metastability depends on

• the presence of some charge and the electromagnetic fields
• rotation of the two throats around each other (like in Earth-Sun or the LIGO black hole pairs before mergers)
• the presence of massless Weyl fermions whose motion is described by Landau levels

You can see that there are some "unusual" building blocks that may justify why this kind of a solution hasn't been found before – or why people could have claimed to have proven that some classes of traversable wormholes were impossible.

The object isn't quite stable because the orbital motion emits gravitational and electromagnetic waves, the distance between the throats is decreasing, and the two sides eventually collide and merge.



Maldacena wouldn't be the real main father of the ER-EPR correspondence if he didn't discuss it in this context. So the authors claim that this system – even though the wormhole is traversable, unlike those in the original ER-EPR correspondence – is equivalent to a pair of entangled black holes. Those must be near-extremal charged black holes.



Today it's a rather good day to talk about entangled near-extremal black holes because of the new paper by Miguel Montero (Leuven) who claims an entanglement-based proof of the Weak Gravity Conjecture within an AdS space. As we noted in the original paper, the Weak Gravity Conjecture is – under certain conditions – equivalent to the instability of the non-supersymmetric extremal charged black holes.

Despite the classically vanishing temperature, these black holes should better have a way to decay "at least a little bit and slowly", otherwise there would be too many microstates and their loop effects could produce lots of troubles etc. When extremal black holes decay, their charge shrinks by a higher percentage than their mass (because they can't go super-extremal) – so the particle they emit must obey the opposite inequality. And the particle they emit must therefore be "lighter than how much charged it is", in the units where \(M=Q\) means "extremal", and the self-interaction between two such particles therefore establishes that gravity is weaker than the electric force.

Montero considers such objects in the AdS space and the entanglement between these objects or the regions they occupy. He resolves an apparent paradox but during the resolution, he realizes that a general information-theory inequality involving entanglement entropies has to be obeyed, and this inequality may be translated to the Weak Gravity Conjecture.

There seem to be interesting things that you can do with pairs of entangled objects, even charged or rotating or orbiting ones, and you shouldn't be afraid of playing with these composite objects. On top of that, Montero's work – if right – is a rather novel type of reducing "forces and dynamics" to "pure quantum information".

Note that in quantum gravity, the area (a dynamical variable in general relativity) is identified with the entropy (some information). Ted Jacobson is often associated with a more general derivation of Einstein's equations from the flows of entropy. Here, other physical objects such as forces as being linked to the entanglement entropy, i.e. information.

Because string theory – and/or probably any consistent quantum theory of gravity – unifies gravity with all other forces, and because Einstein's gravity may be translated to entanglement-like variables, it looks like "all of physics" may be translated to entanglement-like variables. Doesn't this statement produce an immediate contradiction? We seem to say that even the spacetime where physics takes place is encoded in the information but the information may only be carried by objects that are located in the spacetime in one way or another.

I think that it is enough to look at the known examples to see that the pre-existing spacetime is never "quite" eliminated from the picture. Instead, the examples support my picture of the "background indifference". You may pretty much start with any "background" you want and by doing something with it, you may describe any close enough background (including those with different topologies). But quantum gravity isn't a "vacuous enterprise involving information". Instead, quantum gravity is the set of all maps how one spacetime configuration may be linked to almost any other.