# Are black holes eternal?

The popular description of Hawking radiation with one particle from a virtual pair falling in and the other escaping is just a pretty picture (although Hawking uses it in a 1976 paper), "*in another model, the process is a quantum tunneling effect, whereby particle-antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon*". In fact, one does not even need the first particle to fall under the horizon. The radiation will still be observed if it just gets stuck asymptotically approaching it, while its companion acquires escape velocity and leaves the black hole's gravity well. The problem is that proper description must involve quantum gravity, which does not exist yet, since we have both quantum particles and very strong gravitational field in the picture.

What Hawking and others do is semi-classical gravity, where the metric is classical and described by general relativity, while radiation is quantized. Considering that such quantum/classical coupling is known to contradict the uncertainty principle (see Ricles, p. 37) one should not expect too much in the way of consistency in details, even if the result is qualitatively correct. For now, "tunneling" works. But considering how little the actual QFT picture of light propagation in a medium say, resembles both classical and semi-classical descriptions of that, it is likely that quantum gravity picture, when we have it, will be similarly different.

The virtual particle picture comes from Feynman diagrams in perturbative expansions of QFT. It is well known that gravity does not mix well with perturbative expansions because of divergencies (Ricles, p.46), so particle description may break down altogether near the event horizon. Alternatively, when gravity is quantized, the horizon may fluctuate like Wheeler's quantum foam and absorb particles that are classically strictly above it. It often happens that semi-classical calculations approximate the correct answer mathematically, but the physics they suggest is overly naive. We know that for modeling light in a medium, and for Bohr's model of the hydrogen atom for example.

Lots of questions here, I can answer a few of them.

The question might sound very easy - Hawking radiation, however I was pondering that as you get closer and closer to a black hole, time dilates exponentially where the surface of the black hole is "timeless".

So how can anything even anti-matter destroy a black hole if it cannot touch the surface however close it gets to the black hole?

Easy part first:

A black hole eats antimatter as easily as matter. Now in the known universe, matter is much more common, so in an accretion disk as matter falls into a black hole, antimatter would do what it always does, touch a corresponding matter particle and create a poof of gamma rays. Now if space is empty, antimatter would get eaten by a black hole in exactly the same way matter particles are. There would be no noticeable difference.

Hard part: The "nothing can fall into a black hole". There's a few topics on it, linked below and, I've tried to understand on an intuitive level and it still doesn't make sense to me.

If you fall into a black hole, when do you go past the event horizon and Can matter really fall through an event horizon

Moving on:

Or is it to do with wave-particle duality? If it is the case then do we treat micro-black holes with different rules as other fundamental forces might cause different behavior at the scale?

Micro black holes probably don't exist, but it's the same set of rules. The reason Micro black holes in theory, radiate hawking radiation much faster is because, the gravitation drops off far faster, so it's easier for a particle-anti particle pair to split and have one escape, the other not. With a stellar mass black hole, it's far more likely that both of the particle pair do the same thing, either they both stay outside and erase each other or they both fall inside. - keep in mind, were only talking about particle pairs that appear outside the event horizon where one might stay outside and fly away and the other might fall inside. Pairs that appear inside both likely stay inside.

Next, how can "virtual" particles get absorbed into the black hole if the particle can never reach there? Or again is it due to wave-particle duality

I'm not sure what you mean by wave-particle duality in this situation, but the quick and dirty explanation of how hawking radiation works (my limited understanding), is the virtual particle-anti particle pair form outside but close to the black hole's event horizon, and one of the two escapes while the other of the two goes towards the event horizon. It doesn't really matter much if the 1/2 that doesn't escape flies towards but stays outside or flies towards and flies inside. What matters is that 1/2 flies away. That's the 1/2 you care about, cause that becomes a real particle. But as Conifold points out, this is a theory, not a certainty.

even if it then due to statistics if there is 50% chance of anti-particle (as there is particle and anti-particle) falling and destroying equivalent mass of black hole thus reducing its mass, then there must also be another 50% if normal mass falling in and thus adding to black hole mass and if we extrapolate this over trillions of years the black hole must still remain stable mass because over time the statistics add up and equal amount anti- and normal matter fall in thus there should be no realistic change in mass. If not why does gravity more strongly pull on anti-particles?

Gravity doesn't pull harder on anti-particles and anti-particles aren't negative mass. both particles and anti particles are positive mass. What happens (and I'm going to butcher this, but I can only explain it the way I look at it), but what kind of happens, is that the particle-anti particle pair are both positive mass but (see here) https://en.wikipedia.org/wiki/Virtual_particle

Quote:

A virtual particle does not necessarily appear to carry the same mass as the corresponding real particle. This is because it appears as "short-lived" and "transient", so that the uncertainty principle allows it to appear not to conserve energy and momentum. The longer a virtual particle appears to "live", the closer its characteristics come to those of an actual particle.

and, I should quote this as well:

Many physicists believe that, because of its intrinsically perturbative character, the concept of virtual particles is often confusing and misleading, and is thus best avoided

and this:

A virtual particle does not precisely obey the formula m2c4 = E2 − p2c2.[7] In other words, its kinetic energy may not have the usual relationship to velocity–indeed, it can be negative.

So, it doesn't matter if the particle that escapes is a particle (normal matter) or an anti particle (anti matter) cause both have mass, so what you have is essentially a vacuum, right outside the event horizon, creating and spitting mass away from the black hole, and concervation of mass requires that the black hole lose mass.

How does this happen? Erp, well, uh, er, something to do with quantum tunneling and negative kinetic energy, and, I don't get that either, but in both cases, a particle or an anti particle flying away from the black hole, mass leaves the black hole (in theory)

Think of it this way, and I'm not sure this is right, but lets pretend there's a gazillion particles just outside the event horizon, in ultra slow time dilation, falling towards the singularity slower and slower, and you have the quantum fluctuation and a particle/anti particle pair form just outside of that - one of the particle anti particle flies off and becomes a real particle, the other of the pair, wants to vanish cause it has negative kinetic energy and it's not real anyway, so it meets one of the real particles outside but falling very slowing towards the black hole and they both disappear - in effect, mass disappears that's falling towards the event horizon and mass appears that flies away from the black hole.

That's probably not a good way to look at it, I'm just kind of throwing it out there.

You might also want to read this, also from the Wiki article on virtual particles, linked above:

Paul Dirac was the first to propose that empty space (a vacuum) can be visualized as consisting of a sea of electrons with negative energy, known as the Dirac sea. The Dirac sea has a direct analog to the electronic band structure in crystalline solids as described in solid state physics. Here, particles correspond to conduction electrons, and antiparticles to holes. A variety of interesting phenomena can be attributed to this structure. The development of quantum field theory (QFT) in the 1930s made it possible to reformulate the Dirac equation in a way that treats the positron as a "real" particle rather than the absence of a particle, and makes the vacuum the state in which no particles exist instead of an infinite sea of particles.

So, what you have, or at least one way of looking at it, is space is full of negative energy and positive mass - the combined energy is zero, but negative energy is a property of space, and if a virtual particle escapes and becomes real - there's a corresponding negative energy left where that particle came from.

(and a lot of what I wrote might be wrong, but I thought I'd give it a shot to try to explain and answer some of your questions - I've given this a fair bit of thought as I find it fascinating myself).

Finally how can black holes be destroyed by it emitting light? If a black hole sucks light how can it be emitted?

This is kind of covered above, but black holes aren't destroyed by emitting light, they very very very slowly evaporate because the space just outside of the black hole can create real mass that flies away from the hole and negative energy that gets absorbed by the black hole - or, something a little bit like that anyway. :-)