# Why aren't black holes antimatter fountains?

As I understand it, nothing can escape a black hole because the only worldlines leading 'out' from the event horizon point backwards in time.

As I understand it, antimatter is time-reversed ordinary matter.

If the worldline of an ordinary particle points towards the singularity, this is the same as the worldline of its antiparticle pointing away from the singularity (viewed from the opposing direction).

Therefore the "forward" facing worldline of an antiparticle always points away from the singularity.

So why aren't black holes - especially massive ones - constantly spewing out antimatter?

I know that the answer is something along the lines "that isn't what CPT means/that isn't how black holes work," but I've only ever recieved the popular science explanation of either of these, so I'm not clear on exactly where the error is. I would appreciate a more in-depth explanation.

• The glib popsci-level answer is that when you apply time reversal, you have to reverse everything. When you time reverse matter falling into a black hole, you get antimatter coming out of a white hole, not antimatter coming out of a black hole. And that's fine because everything can come out of a white hole. – knzhou Nov 19 '19 at 23:10
• When people talk about time reversal they often fail to mention you have to reverse the spacetime too, because you usually work in flat spacetime, where this does nothing. But in GR, discrete symmetries like time reversal are trickier. (In fact, usually a time reversal operation doesn't even exist at all.) – knzhou Nov 19 '19 at 23:11
• @knzhou Well that certainly clears things up. What does global time reversal look like? Is it just changing the sign of the metric, or do you need to do more? – R. Burton Nov 19 '19 at 23:26
• Antimatter is just like regular matter but with an opposite charge. Wouldn't time reversed matter be with negative mass instead? – Krumuvecis Nov 20 '19 at 0:46
• @R.Burton Your question doesn't require black holes. Consider a rain on the Earth. Droplets of matter (water) fall down. According to your logic, this is the same as droplets of antimatter raising up from the ground to the clouds. So why isn't the Earth an antimatter fountain? – safesphere Nov 20 '19 at 6:51

So this is really the twist in the construction of QFT that is still sometimes misunderstood. Historically, people like Dirac noticed that solutions to relativistic field equations such as the spinor equation for $$\psi(x)$$ admitted apparent negative mass-energy densities. However, once you go into QFT, either from a "second quantization" or a Fockian bottom-up construction, you realize that these were never negative energy densities, it is just that $$\psi(x)$$ represented a "mirrored mix" of creation operators of one type of particles and annihilation operators for their "mirror buddies". This means that operators such as $$\psi(x)$$ acting on a state would create a particle at $$x$$, and destroy its mirror buddy, if it was at $$x$$.

Long story short, "mirror buddies", also known as "antiparticles" are absolutely and definitely particles with positive energy, the same as "ordinary particles", and they cannot spring into existence without a positive source of energy. (Let's not talk too much about "virtual particles" which allow quantum weirdness influence interactions just because of the "possibility of particles/antiparticles being there, if enough energy was present".)

More specifically, the construction of QFT requires postulating a vacuum, and its definition is that you cannot just freely pump more positive-energy particles/antiparticles from it, since negative energies are not allowed. This assumption might not be obvious, but it is actually simply the only choice that allows you to obtain any useful predictions from the theory. And one last thing - there is no meaningful way in which a positive energy particle travelling forward in time can be distinguished from a negative energy particle travelling backwards in time. So you could say all the matter falling into a black hole is negative-energy matter traveling backwards in time. But you will never see a positive energy particle travelling backwards in time out of a black hole.

The reason why antiparticles can sometimes be referred to as "time-reversed particles" is a bit subtle and has to do with Lorentz symmetry, particularly CPT. It is just that you are allowed to build theories which have time-irreversible processes while staying Lorentz-invariant as long as you have those "mirror buddies" in the game as well. The point is that the theory does not need to allow the identical time-reversed processes with the original particles, it just needs to allow identical time-reversed processes with their mirror buddies (and possibly also reversed parity).

I kind of understand where you are coming from with this question - it really goes back to the popular understanding of the creation of Hawking radiation by virtual particle-antiparticle pairs. But in this explanation it is not important that the particle going "in" is an antiparticle, while the one going "out" is a particle. You can swap those two and, indeed, Hawking radiation is made of both particles and antiparticles. What allows Hawking radiation is the "quantum weirdness" that allows the quantum principles to virtually "borrow" energy-momentum and transfer it over space-like intervals if it is energetically favorable. In the language of virtual particles, it is a particle-antiparticle pair either of which is executing the transport in either direction.

Without going any deeper into the details, I just want to point out that the only thing that allows the black hole to "leak" particles is the breaking of time reversal by the collapse. A perfectly time-reversible computation actually yields no radiation (which was actually computed by Unruh some time before Hawking). So really Hawking radiation is created despite CPT symmetry.

• There are future-pointing negative energy states inside black holes, and those are essential for Hawking radiation. – A.V.S. Nov 20 '19 at 17:41
• @A.V.S. Yes, if you define energy with respect to $t$ or generally with respect to the domain of outer communication. But the energy is not negative with respect to any local notion of vacuum inside the black hole. – Void Nov 20 '19 at 20:26

When you time-reverse a black hole, you get a white hole. Therefore you don't see black holes as antimatter fountains. White holes would be antimatter fountains, but that doesn't say much because everything falls out of white holes anyway.