In the octonionic theory, why does a black hole radiate?

Are split octonions connected with black hole space-times?!

The context is that fermionic states can be defined using octonions, and using split octonions. A fermion lives in 8D space.

Octonions have signature (8,0) whereas split octonions have signature (4,4).

Black holes arise from the spontaneous localisation of fermions (i.e. octonions) when the gravitational radius of the system exceeds its effective Compton length.

We well know that in the interior of a black hole, space and time interchange roles. Could it then be that a black hole spacetime [interior + exterior] is the limiting case of a split octonionic space-time?

Assuming that it is, we ask the question:

In the octonionic theory, why does a black hole radiate?

In this theory, fermions are defined in 8D octonionic space using octonions and split octonions.

Elementary particles and black holes are the opposite limits of fermionic entities: particles are the quantum dominated limit, whereas black holes are the gravity dominated limit. There are two competing length scales associated with a collection of entangled fermions. A gravitational length scale Lg and an effective Compton length Lq, which obey Lg x Lq = L_p^2, where L_p is Planck length.

Non-black hole non-elementary particle entities such as stars and other classical macroscopic objects are entangled fermions caught mid-way between elementary particles and black holes - their proceeding to the BH state being slowed down by standard model forces. For now we can ignore these forces and focus only on elementary particles and black holes.

Quantum systems are those in which the effective Compton length exceeds the gravitational radius. And just the reverse for black holes.

In the trace dynamics of the octonion-valued fermions, a quantum system with no entanglement is at statistical thermodynamic equilibrium. It has maximum Boltzmann entropy.

Entanglement moves the system away from equilibrium, towards classicality, thereby reducing it's entropy. Entanglement is order; no entanglement is disorder. Entanglement reduces the effective Compton length while increasing the gravitational radius. Critical entanglement is when the gravitational radius becomes larger than the Compton length, the quantum-to-classical transition is competed, and the black hole forms. This is a non-equilibrium state, and the high entropy of the black hole notwithstanding, the entropy of the system is now lower than what it is when it is completely unentangled [thermodynamic equilibrium]. This is why a black hole radiates; it is attempting to disentangle and return to equilibrium.

We note that this quantum-to-classical transition is governed by the degree of entanglement; this physics is independent of energy scale. In the expanding very early universe, an energy scale shows up because only when the expanding universe has cooled sufficiently, critical entanglement becomes possible. But the key physical role is of degree of entanglement, not of energy.

Why does entanglement lead to classicality? In the octonionic theory, the Hamiltonian also has an anti-self-adjoint (ASA) part. This ASA is negligible when there is no entanglement, the self-adjoint part dominates, we have unitary quantum evolution and the equivalent of thermodynamic equilibrium. The system lives in an 8D octonionic space.

Entanglement enhances the ASA part relative to the self-adjoint part, bringing in some non-unitary component to the unitary evolution. Critical entanglement is when the ASA becomes dominant over the SA, spontaneous localisation breaks unitarity, and the black hole forms. This classical object is confined to a (coarse-grained) 4D subspace of the 8D octonion space (this 4D being the black hole interior). The black hole exterior is the other 4D half of the (coarse-grained) octonion subspace - it is our 4D spacetime. The split octonions are playing a role here.

What then of the information loss paradox? Conventional studies take a black hole as given a priori and then ask if the complete evaporation of a black hole into thermal Hawking radiation violates unitarity?

We would like to look at this process differently, and ask how did the black hole form in the first place? The initial state [thermodynamic equilibrium] has no information: maximum entropy, no entanglement. Entanglement is gain of information, reduction of entropy. If we remove observers from the scene, and consider the BH interior as well as exterior [the full 8D octonionic space] we know the information content. It is determined by the entanglement. By radiating, the BH is disentangling, spontaneously unlocalising, increasing entropy, and going back go equilibrium. The black hole is a far from equilibrium system, confined to the 4D subspace of 8D octonionic space (as if the molecules of gas in a box have all landed up in one half of the box). Gravitation is an emergent, far-from-equilibrium, thermodynamic phenomenon. By evaporating, the black hole is returning to the full 8D octonionic space, and returning to the unentangled equilibrium state.

(I) We began with zero information (no BH), (II) gained information (BH formed) and (III) went back to zero information (complete evaporation). The information loss paradox arises if we ignore step I and straightaway start at step II. But we must necessarily ask how the black hole got there in the first place? When we do that, we find there is no paradox.