How do you “create” an event horizon?

(I’ve not bothered to really edit this, sorry)

As far as I can tell, black hole event horizons cannot just be suddenly created in a single instant across an area of space-time. As with pretty much everything we know, they too much evolve.

If we take it to be true that Hawking radiation is produced as a result of event horizons resulting from harsh spacetime curvature, and if this results in the production of positive and negative energy from the vacuum, then it must be the case that this radiation starts being produced at the very moment an event horizon begins to form, no matter how big or how small.

How then do we make sense of this in a time reversal?

Radiation would then coalesce into an event horizon. Meaning, the creation of matter spontaneously (from where it would otherwise return to the vacuum, eating away the mass of a black hole) from the vacuum would produce positive and negative energy. The positive energy would stay to form the central mass-energy of a black hole. The negative energy would then fly out (with just barely enough momentum) to meet incoming positive energy Hawking radiation coalescing at an event horizon, where they would collide and return to the vacuum, leaving the positive energy of the black hole that supposed curve space-time.

Yet, the only way the negative energy could fly out to meet the time-reversed incoming positive energy Hawking radiation, would be if the event horizon changed just as the two particles were about to meet, thus allowing them to meet. And in a sense, these two particles coming together will have their own apparent event horizon, a point beyond which they cannot avoid returning to the vacuum.

But how does the time-reversed event horizon change as this Hawking radiation returns to the vacuum? If a black hole evaporates, then that should imply it’s horizon is presumably shrinking because it’s radiating & losing mass. In a time reversal, the event horizon would be growing. This means that as reversed-time increases, the negative energy particle flying outward approaches what is an expanding event horizon. And for some reason, the positive energy photon stays at the center (the singularity) having presumably converted to positive rest-mass. If these are positive and negative virtual photons, then their velocities are always a constant c.

The evaporation rate of a black hole increases the smaller it gets. Therefore, the time-reversed evaporation would experience as slower and slower event horizon expansion rate as the negative energy photon flies outward to meet it’s partner. These two time-reversed photons would then meet to annihilate precisely at the event horizon.

The positive energy photon would be traveling from an area of more or less flat curvature to an area of more curvature at the event horizon. This means it would be blueshifting to higher frequency from the perspective of an observer at the horizon. To an outside observer seeing any scattering (outbound photons) off an object falling towards and just ouside the event horizon, this object would appear to be infinitely redshifing (time stopping, standing still at or just before crossing the event horizon). Meanwhile, the negative energy photon, if it approached the horizon from within the black hole, would seem to have travelled from an area of significantly more (infinite) curvature near the singularity (relative to an outside observer), to an area of relatively less curvature at the event horizon. This means that to an observer at the event horizon, the negative energy photon would appear to be redshifting down from an infinitely blue frequency while the incoming external positive photon would be blue shifting from an infinitely redshifted origin. Note that hypothetical singularity at the center of the black hole is the point of infinite curvature (relative to an outside observer), whereas the the event horizon is simply the part of the curvature that supposedly prevents escape as observed from the outside.

Therefore, the outside observer might assume to know what it looks like at the event horizon and conclude that the negative outward particle should be redshifting (infinitely so) from it’s original (more blue) energy state, until it collides with it’s positive partner falling towards the event horizion, and blueshifting in the process to a point where each photon is of equal energy and opposite energy. Each Hawking radiation particle should then have opposite spin and opposite, yet equal, energy. From the perspective of an outside observer, they would then collide at their at infinitely red redshift, precisely at the event horizon, where they annihilate leaving zero energy. An observer at the horizon would not actually see these particles at all because observing them would prevent their annihilation. In the time reversal, it is then at this point that an observer would assume that the disappearance of an unobserved positive Hawking radiation photon and an outward negative energy photon annihilating is conserved by the remaining positive energy that adds to the mass of the growing/feeding black hole. In this way, an observer at an established event horizon might not see anything special as the black hole grew, other than perhaps the lensing created by a change in the curvature.

On the other hand, in the case of the supposed birth of a black hole, if they are every really born, what would an observer see sitting precisely at the event horizon going from no event horizon to the first beginnings of one?

Perhaps another way to look at this time-reversal might be to assume that the black hole is a 2-sphere of negative energy sitting or stuck precisely at the event horizon, waiting for positive energy to come along. It is only when positive energy crashes into the negative energy event horizon that the annihilation of time-reversed Hawking radiation can return to the vacuum in order to grow an event horizon by immediately converting to positive rest-mass energy at the center (the singularity), or spreading it equally around the 2-sphere event horizon.

The event horizon is called an event horizon because it is defined purely by the potential for events to either occur or not occur. The nature of this distinction is entirely relative and observer-dependent. In the time-reversal, this event horizon is defined by the point at which a negative energy Hawking radiation virtual photon meets it’s partner to annihilate. This is defined by the point where they return to the vacuum at the same point at which an original positive energy partner can be observed to remain as positively conserved “gravitating” rest-mass energy.

Going back to the original question, a time-reversed evaporating black hole shares an obvious symmetry with what an observer might appropriately call the “creation” of an event horizon. You throw some positive radiation towards an event horizon and when it meets some negative energy along it’s 2-sphere, you then forever lose your positive energy photo beyond this event horizon.

There is another event horizon that shares some of the same traits, that being the observable universe horizon as a result of observed dark energy expansion. Due to this observed expansion, the assumption is that there would be an observable event horizon beyond which radiation traveling directly to an observer would have no hope of ever being received. As we lose causal contact with inwardly falling photons (pointed directly at us), due to the observed expansion of space, at least for a photon (which we’re free to call negative), it’s “loss” could be considered to be not unlike the meeting of an external positive energy particle precisely at these causal limit of observation (an event horizon).

Perhaps it’s not so strange then to look at the observed dark energy expansion of space as being similar to the time-reversed evaporation of a black hole whereby, instead of expansion, all of our outwardly falling negative energy just barely makes it out of our observable universe where it then returns to the vacuum, encountering positive energy sitting at an observable boundary.

The only issue with his picture, which seems to distinguish it from a classical black hole, is that our universe appears to be closed with no center (whereas the black hole is presumed to have a singularity at it’s center). Therefore, the observable universe is considered to just be a limit for each observer. Each galaxy would have it’s own observable horizon. The best way to picture this is to consider that our reality (including all galaxies & all causal bubbles) would reside on the surface of a 2-sphere as this closed surface has no observable center.

What then is the time-reverse of our observable universe event horizons?

This is inflationary Big Bang cosmology, obviously. Here you have very similar issues arise in terms of causality. We have guessed at an inflationary period to account for observed homogeneity across large distances. We also assume that inflation occurred fast enough to have magnified quantum fluctuations (virtual particles) leading to energy density differences seeding the formation of galaxies. This implies that the Big Bang inflationary period was the point at which observable event horizons emerged as areas of this center-less reality first lost causal contact with one another during an expansion.

What if there was no accelerated inflation leading to the loss of causal contact? Without a huge inflationary period, a hypothetical transparent version might have presumably been a specific size with a specific rate of expansion, whereby every location in a hypothetical 2-sphere universe was just barely in contact with it’s most distant parts (the diameter of a 2-sphere). That is to say that for a 2-sphere with radius r=0 at t=0, an expansion rate of r/t=1 could have accelerated such that a photon traveling at a fixed (πr2)/t=1 (a semi-circle) from r=0 to r=1, would have just barely made causal contact with a most distant patch (the point of the 2-sphere opposite it’s origin at πr2, where it would presumably meet it’s equal & opposite virtual anti-partner), before further expansion causes an apparent event horizon to emerge at every point on the surface. Basically, the total casual contact is only maintained either limited to t=0, or if r either stays constant at t=1 or decreases.

Big Bang cosmology supposes that some point in inflation the universe was able to cool down enough that the relativistic energies carried by initial fundamental particles was no longer big enough to create new proton and anti-proton pairs from the vacuum when collided. This lead to mass annihilation, leaving an asymmetrical reminder of rest-mass due to unknown reasons. At this the point, the density of photons was most numerous. As things cooled further, protons and neutrons were cool enough to form the first atomic nuclei. Eventually, the rest-mass density of the universe begins to gravitationally dominate the photon density. Electrons then started combining with atomic nuclei, to form the first atoms. At around 379,000 years, the universe becomes transparent enough for photons to avoid hitting anything, giving us the CMB radiation we see today.

For photon causal contact to have been lost when the CMB was created at 379,000 years (not that it was), the universe would have had to have an equivalent 2-sphere radius of 60,319 light years. For the universe in this Big Bang inflationary model, the lost of causal contact we’re talking about is presumably not related to photons traveling straight in transparent space, but rather a much slower delayed acoustic type wave comprised of colliding particles in an opaque soup. This means that the universe 2-sphere radius could have been much smaller while having supported the emergence of the first event horizons prior to the CMB phase transition (clearly showing density fluctuations and possible large scale structure).

The time-reverse of this is to compress the universe and heat it up due to rapid deflation, deteriorating atoms, increasing the density of photons, and giving rest-mass enough energy to produce gobs of particles from the vacuum, giving rise to a phase transition where, because of it’s density (at some given size & temperature), universal causal contact is presumably possible such that there are no event horizons, leaving you a uniform singularity.