Hawking radiation and black hole evaporation

[arthwollipot]

Okay. Here's hoping to hear from some of you theoretical physicists and cosmologists.

Particle-antiparticle pairs are popping into existence all the time, but the energy of the universe as a whole is conserved because they annihilate each other quickly. When this occurs near the event horizon of a black hole, one particle can be sucked into the black hole while the other escapes as Hawking radiation.

Now, I've heard several times that this is the reason why black holes will evaporate over time. But that doesn't make sense to me - the black hole isn't losing mass or energy in this transaction, it is gaining mass from the particle that's swallowed up. The Hawking radiation can't carry away any of the black hole's energy, because whatever it carries away ought to be exactly balanced by the particle that is swallowed.

I'm clearly misunderstanding something here. Any help for someone with a non-mathematical background?

 

[Vermonter]

I'm not a scientist, but I'm a huge astronomy and cosmology buff and I've taken multiple college courses on the subject.

Virtual particles are thought to exist everywhere. They pop in and out of existence so quickly that they there's no net gain or loss - they annihilate each other nearly instantly. I have read it as being something of a "foam" of virtual particles bubbling forth.

Anyway.

When a pair of virtual particles appears near a black hole, sometimes the black hole will attract one of the particles before the pair can annihilate each other - this action makes them "real" particles instead of virtual, and thus costs energy to do so. A tiny amount, but it's still an energy deficit. Virtual particles "borrow" energy when they initially appear, and since they typically annihilate each other it cancels out.

This evaporation process takes an extraordinarily long time (beyond the current age of the universe), but it accelerates as the mass of a black hole decreases. I have read that if a black hole is under a certain threshold, it will evaporate quickly due to this process. It's really cool stuff.

 

[GlennB]

My deep research (skimming the wiki article ) suggests it's the anti-matter particle that disappears into the black hole while the matter particle is ejected, with the net effect appearing to be that the black hole gets lighter by ejecting the 'matter' particle.

The true depth of my ignorance of the subject is revealed by the I get wondering why the anti-matter gets sucked in preferentially.

 

[Roboramma]

My deep research (skimming the wiki article ) suggests it's the anti-matter particle that disappears into the black hole while the matter particle is ejected, with the net effect appearing to be that the black hole gets lighter by ejecting the 'matter' particle.

The true depth of my ignorance of the subject is revealed by the I get wondering why the anti-matter gets sucked in preferentially.

Even if that were the case, anti-matter still has positive energy.

The mass of an electron and a position are the same.

 

[rjh01]

Here is another way to look at it. For a very small black hole you cannot say a particle is definitely inside the black hole because its position is an area that includes outside of the black hole. If that particle is outside of that black hole it can escape. Remember you can never give the exact position of a particle.

The implications of this are that the smaller the black hole the hotter it is. A black hole will eventually be very hot and lose all of its energy (mass) in a flash.

 

[Craig B]

Here is another way to look at it. For a very small black hole you cannot say a particle is definitely inside the black hole because its position is an area that includes outside of the black hole. If that particle is outside of that black hole it can escape. Remember you can never give the exact position of a particle.

The implications of this are that the smaller the black hole the hotter it is. A black hole will eventually be very hot and lose all of its energy (mass) in a flash.

I write as a lay person sunk in deep ignorance. But it's wonderful how gravity works backwards. The more energy you take out of a gravitational system, the faster things go, or the hotter they get!

 

[Vorpal]

Warning: handwavy yet technical explanation below.

The Hawking radiation can't carry away any of the black hole's energy, because whatever it carries away ought to be exactly balanced by the particle that is swallowed.

Background: whenever definable, energy is the time-component of the energy-momentum four-vector, while (more ordinary) momentum consists of the spatial components.

For the case of the Schwarzschild spacetime, the Schwarzschild time is a Killing vector field ∂_t, which is what provides energy conservation for particle orbits: if the energy of the outgoing particle at infinity is ε, then for any part of its orbit with four-velocity vector u, ε = -∂_t·u = (1-2m/r)(dt/dτ).

Only that's not quite right across the horizon, because the Schwarzschild time is actually spacelike within, with Schwarzschild radial coordinate being timelike instead. This is obvious from the switcheroo the signs of the metric coefficients do at the horizon for the Schwarzschild metric at r = 2m. Thus, for a particle inside the horizon, what a far-away stationary observer considers energy is 'actually' spatial momentum, and thus has no particular problem with being negative.

The true depth of my ignorance of the subject is revealed by the I get wondering why the anti-matter gets sucked in preferentially.

It doesn't. Also, unless the black hole is small, only electromagnetic radiation is relevant, for which particle/antiparticle distinction doesn't even really make intrinsic sense (or rather, photons are their own antiparticles). (ETA: Unless some neutrinos are really, really close to massless, I suppose.)

 

[lenny]

Particle-antiparticle pairs are popping into existence all the time, but the energy of the universe as a whole is conserved because they annihilate each other quickly.

I find it safer to drop the notion that the energy is conserved. It is constantly bubbling about within the limits of the indeterminacy relations.

When this occurs near the event horizon of a black hole, one particle can be sucked into the black hole while the other escapes as Hawking radiation.

The vision of a pair as two balls on a spring that pop into existence, move apart, come back together, and annihilate with each other is also misleading; foam is better. Or Some crazy Dance floor packed solid with people (red shirts and blue shirts) who rarely leave the floor with the partner they entered with (this analogy is still too "particle-like" but beats the two balls on a string; when the particles are identical there is no sense in the phrase "leave the floor with the partner they entered with")

Now, I've heard several times that this is the reason why black holes will evaporate over time. But that doesn't make sense to me - the black hole isn't losing mass or energy in this transaction, it is gaining mass from the particle that's swallowed up.

The picture you describe can be patched up by thinking of the "virtual" particle that "falls into" the hole as annihilating with a "real" particle "inside" the hole. Leaving its original co produced partner free and outside the hole.

But "particles" do not have little labels on them saying "I was just created in a fluctuation and have to annihilate soon". Or ."I am a real particle trapped within this bloody black hole". They are not billiard balls. So that entire picture is potentially misleading, hence all the scare quotes.

Does that help?

 

[dlorde]

Does that help?

It helped me, thanks - I couldn't follow Vorpal's explanation

 

[phunk]

Okay. Here's hoping to hear from some of you theoretical physicists and cosmologists.

Particle-antiparticle pairs are popping into existence all the time, but the energy of the universe as a whole is conserved because they annihilate each other quickly. When this occurs near the event horizon of a black hole, one particle can be sucked into the black hole while the other escapes as Hawking radiation.

Now, I've heard several times that this is the reason why black holes will evaporate over time. But that doesn't make sense to me - the black hole isn't losing mass or energy in this transaction, it is gaining mass from the particle that's swallowed up. The Hawking radiation can't carry away any of the black hole's energy, because whatever it carries away ought to be exactly balanced by the particle that is swallowed.

I'm clearly misunderstanding something here. Any help for someone with a non-mathematical background?

The energy isn't lost in the particle being consumed by the black hole. It's lost in separating the particles to make them real, then half is gained back when one falls into the black hole.

 

[Roboramma]

I can understand the fact that energy is given off. I don't get how it's conserved. Why, when a particle falls into the black hole, does the mass of the black hole decrease. I still don't see it.

Yes, energy is conserved, but why? Shouldn't the infalling radiation be exactly the same as the outgoing Hawking radiation?

Someone said that the infalling particle will annihilate with a particle inside the black hole. Whatever allows that to happen should allow the outgoing particle to annihilate with a particle outside the black hole, since there's no difference between the particles.

I know that in order to understand I'd probably have to understand the mathematics, but that's really just saying that the explanations so far aren't good enough! (for me )

 

[Roboramma]

Only that's not quite right across the horizon, because the Schwarzschild time is actually spacelike within, with Schwarzschild radial coordinate being timelike instead. This is obvious from the switcheroo the signs of the metric coefficients do at the horizon for the Schwarzschild metric at r = 2m. Thus, for a particle inside the horizon, what a far-away stationary observer considers energy is 'actually' spatial momentum, and thus has no particular problem with being negative.

Why doesn't the same logic apply to real particles? In which case it seems that if I shine a light into a black hole the energy could become negative momentum and the black hole could grow smaller, rather than larger?

 

[phunk]

I can understand the fact that energy is given off. I don't get how it's conserved. Why, when a particle falls into the black hole, does the mass of the black hole decrease. I still don't see it.

It doesn't decrease when the particle falls in. It decreases when its tidal force tears apart the virtual pair. The energy is lost via gravitation, not the infalling particle.

 

[Roboramma]

It doesn't decrease when the particle falls in. It decreases when its tidal force tears apart the virtual pair. The energy is lost via gravitation, not the infalling particle.

Okay, so in that case how does the separation of the particles cause energy loss? And why is the loss directed toward the black hole rather than away?

 

[edd]

I think this may be one of those cases where trying too hard to treat virtual particles like they are particles is going to fail.

 

[Darat]

...snip...

I know that in order to understand I'd probably have to understand the mathematics, but that's really just saying that the explanations so far aren't good enough! (for me )

Don't agree with that, the theory came about as a result of mathematics, so I don't expect that a language such as English should be (or is) capable of describing it "accurately".

 

[Roboramma]

Don't agree with that, the theory came about as a result of mathematics, so I don't expect that a language such as English should be (or is) capable of describing it "accurately".

I agree, there's no requirement that a "good enough" explanation is possible. I was mostly just joking.

 

[Roboramma]

I think this may be one of those cases where trying too hard to treat virtual particles like they are particles is going to fail.

Probably. I have to admit I really don't understand virtual particles. So that's probably the issue I'm having.

 

[Mister Earl]

Let's say I come up with a great way of making large amounts of antimatter. I make enough to form a medium sized planet.

I drop it into the black hole. What happens?

 

[Roboramma]

Let's say I come up with a great way of making large amounts of antimatter. I make enough to form a medium sized planet.

I drop it into the black hole. What happens?

Ignoring any interactions on the way into the black hole, the black hole gets bigger. You can't even tell, once it's in the hole, that it was anti-matter rather than matter.