# Hawking radiation no change to black hole mass?

1. Dec 1, 2015

### waywardtom

have read numerous times about Hawking radiation. don't understand how that can lead to black hole evaporation in so much that wouldn't as many matter as anti-matter particles fall in thus balancing out over time to the growth and evaporation of black holes thus leaving the mass of the balck hole stable?

2. Dec 1, 2015

### mathman

When a virtual pair is created and one particle escapes from the black hole, the mass is reduced. Anti-matter has positive mass, so your observation is not valid.

3. Dec 1, 2015

### waywardtom

are you saying that it is in the maintaining of the single particle, for which energy of the black hole has been depleted rather than one of the twins falling into the black hole which is not considered in this scenario's consideration of black hole mass evaporation?

the creation of the pair has nothing to do with the black hole. the pair comes into existence and fades out preserving the first law. but the properties of the event horizon prevents the annihilation of the pair. so the mass of the black hole is depleted by the energy required to keep the pair forever separate and either a single matter or anti-matter particle in existence. the amount of energy present in the positive matter or anti-matter particle which escapes is equal to the amount of energy depleted from the black hole in doing so. this eventuates in the mass of the black hole over the eons of keeping particles separate eventually being depleted to evaporation of the hole.

okay, if this is sound, then on a following consideration, how does anti-matter have (positive) mass? to me this sounds like saying a negative amount of oranges adds to the value of a farmer's crop yield.

4. Dec 1, 2015

### phinds

That's the "English language" description of what happens but it isn't really quite what happens. Hawking said that the whole "virtual particle pair" thing is just the only way he could think of to use the English language to describe something that you really can only descirbe with the math.

The positive mass of an antimatter particle is perfectly reasonable given that the ONLY thing that makes it "anti" it its charge. This has been confirmed observational.

5. Dec 1, 2015

### Staff: Mentor

On average, yes. Why do you think that would prevent the hole from evaporating? Matter and anti-matter both have positive mass, so antimatter particles in Hawking radiation carry away mass and reduce the mass of the hole just as matter particles do.

6. Dec 1, 2015

### Staff: Mentor

Because there is no such thing as "negative mass".

More precisely, the word "mass" can have one of two meanings here:

(1) Rest mass, or more properly, invariant mass. Antiparticles have the same invariant mass as their corresponding particles, because the quantum transformation that takes particles to antiparticles does not change the invariant mass. And in any case, there is no such thing as negative invariant mass; the invariant mass of every quantum object is either positive (like electrons, quarks, and other ordinary matter particles) or zero (like photons).

(2) Energy. All quantum objects have positive energy. More precisely, the Hamiltonian operator in quantum mechanics is bounded below, i.e., it has a minimum value. The state in which it has this minimum value is called the "vacuum state", and any quantum state that has anything in it, i.e., is not the vacuum, has an energy larger than this minimum. That means the difference between the energy of any quantum object and the energy of the vacuum state, which is the relevant "energy" here, is positive.

7. Dec 1, 2015

### SCSF

Black holes don't differentiate between antiparticles and particles. Any radiation that would be emitted by the reaction between the anti particle and whatever exists inside the black hole couldn't escape from the event horizon anyways.

8. Dec 1, 2015

### waywardtom

when the matter anti-matter pair is created, then permanently split by the event horizon, and so the mass -be it anti-matter or matter- which falls into the black hole thus adding to the mass of the black hole, thus increasing its longevity, is less than the amount of energy lost by energy/mass of the black hole preserving the split through the event horizon?

if the above is correct, how does the black hole know to expend additional mass/energy through gravity -which is being expended anyway by maintaining itself- to keep the matter anti-matter pair separate?

9. Dec 1, 2015

### Staff: Mentor

waywardtom, I can't make sense of your post #8. However, I think you should be aware that the "particle-antiparticle pair is created, one falls into the hole, the other escapes" model of Hawking radiation is heuristic only; the underlying math actually doesn't look much like that at all. One key reason for this model being heuristic is the fact that, as I said in a previous post, real particles all have positive energy, so a real particle falling into a black hole will increase its mass, not decrease it.

In the heuristic model of Hawking radiation, the pair that is created is a pair of virtual particles, not real particles, and has zero net energy when it is created; heuristically, one particle has negative energy and the other has positive energy, and they add up to zero. The hole's gravity then pulls the negative energy particle inside the horizon before it can annihilate with the positive energy particle; the positive energy particle then flies away and escapes. The net effect of this is to decrease the mass of the hole, by effectively transferring some of it to the particle that escapes.

But all of this talk about virtual particle pairs, and one having negative energy, is, as I said, heuristic only; the underlying math doesn't really look like that. So there's a limit to how much understanding you can get with this model. Also, the model can lead you to ask questions that aren't really well-defined, like this one:

The black hole doesn't have to "know" anything. (Btw, it doesn't have to "expend energy through gravity" to maintain itself either; I don't know where you are getting that from, but it's not part of the GR model of black holes.) The underlying process is just a quantum field in curved spacetime undergoing state transitions.

10. Dec 2, 2015

### waywardtom

this is what i deduced, once the virtual particle becomes a real particle, by reason of being permanently separated from virtualness, and falls into the black hole, that mass of the singularity is increased, as you and phinds educated me, be it the particle or anti-particle.

but here you say it is the "negative energy particle" that falls into the hole. 50 50 says over time equal amount of both particles fall in. so if both particles have mass, then either one into the hole increases its mass, thus increases singularity mass.

once permanently separated, don't both particles -anti matter and matter- take on equal amounts of mass? one into the hole the other on its way to eat lunch in albuquerque? and the conservation of energy says then that somewhere energy must equally decrease, so let it be that the energy mass of the singularity must pay, so it decreases by the same amount of energy that equals the matter plus anit-matter pair?

as soon as the virtual pair are sufficiently kept separate by the just severe enough curvature located at the event horizon, at that moment of "whoops too late to annihilation" musn't mass decrease in the singularity equal to the sum of mass created in the opposite now real pair? that event horizon located at a real spacetime distance away from the singularity which contains the mass influencing the spacetime around it. so there is an entanglement of mass/energy within the singularity and the mass/energy virtual to real pair located at the event horizon?

i suppose the the now real matter or anti-matter particle which escapes cannot annihilate the opposite virtual particle of a virtual pair adjacent to it as it escapes? which then cascades into infinity, preventing me from asking this question?

yah, that was a silly question, but remember, there are at least 10 silly questions to every real progression in the advancement of science. its a law. so, 9 more silly questions until my mind progresses! thank you for your kind indulgence!

11. Dec 2, 2015

### Staff: Mentor

Although you will often see Hawking radiation explained in terms of virtual particle pairs with one member of the pair falling into the black hole, that's not really what's going on. There's only so far you can go with that picture.

There's a good layman-friendly summary of the situation here: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

To get a sense of just how much has been left out in what you've been reading, you can try the real thing: http://www.itp.uni-hannover.de/~giulini/papers/BlackHoleSeminar/Hawking_CMP_1975.pdf. The heuristic explanation about virtual particle pairs appears on the fourth page.

Last edited: Dec 2, 2015
12. Dec 2, 2015

### Staff: Mentor

No. That is why I said the "virtual particle" model is heuristic only; you can't draw inferences from it the way you do here.

Because if you insist on using the heuristic virtual particle picture, this is what it says. If you object that "negative energy particle" doesn't make sense, well, that's why we say the virtual particle model is only heuristic.

Equal numbers of particles and antiparticles fall in, but every particle that falls in has negative energy, if you insist on using the heuristic virtual particle model.

At this point I think it's better to drop the virtual particle model, since you're trying to draw inferences from it that aren't valid. Instead, you should check out the links that Nugatory gave.

13. Dec 2, 2015

### martinbn

14. Dec 2, 2015

### DrStupid

Don't overshoot! Keep in mind that uncharged particles may have antiparticles too.

15. Dec 2, 2015

### albert36

A related visualization/approximation DESCRIPTION from Leonard Susskind:
his book, THE BLACK HOLE WAR [My Battle with Stephen Hawking to make the world safe for quantum mechanics]
Pg377: ... "...The picture pf the black hole horizon that was emerging was a tangle of string flattened out onto the horizon by gravity....quantum fluctuations...would cause some parts of the string to stick out , and these bits would be the mysterious horizon-atoms. Roughly speaking, someone outside the black hole would detect bits of string, each with two ends firmly attached to the horizon...these are open strings.....and could break loose from the horizon and that would explain how a black hole radiates and evaporates. It seems John Wheeler was wrong; black holes are covered with hair...

Another viewpoint from Beckenstein: Black holes have temperature, therefore they MUST radiate as do all black bodies. Of course this does not explain the exact mechanism, only that energy will eventually be lost.

Here is a bit more summarizing the Hawking/Susskind struggle:

Black Holes - A Closer look at Hawking Radiation

16. Dec 2, 2015

### waywardtom

thank you PeterDonis, Nugatory, albert36, et al. appreciate your taking time to explain. as much as i want to know how it happens, i don't care too much for the popping of my bubble. :)

17. Dec 2, 2015

### phinds

Good point. Thanks.