# Do black holes evaporate or go bang ?

1. Aug 8, 2005

### jimw

Do black holes "evaporate" or go "bang"?

A TV program last night quoted Hawkins saying (in effect) that, because a small amount of matter/energy escapes from black holes, they will eventually just disappear (evaporate). This raised a few questions to my non-physicist mind: (1) Since black holes "gobble up" matter, wouldn't the rate of increase be greater than the "evaporation" rate? Perhaps eventually there would be nothing left to feed it? (2) If a black hole did evaporate, it seems it would become less dense during the process and should explode when the gravitational force could no longer hold it together densely enough (the opposite of when a star implodes to create a black hole). perhaps a mini big bang?

Does this make sense? Thanks for any feedback.
Jim

2. Aug 8, 2005

### JesseM

Yeah, as long as there's a continual supply of material to feed it a black hole can take in matter/energy faster than it radiates it out. The smaller the black hole, though, the faster it will be radiating energy away.
Actually smaller black holes are more dense than larger ones--you can see from the Schwarzschild formula here that the mass is proportional to the radius, while of course the volume is proportional to the cube of the radius, so mass/volume will decrease as radius increases (the black hole may evaporate when it reaches the 'Planck density', as discussed in this thread). So, a large black hole could have an arbitrarily low density. As for what happens at the moment the black hole evaporates, http://www.einstein-online.info/en/elementary/quantum/evaporating_bh/ [Broken] says that "For black holes with lesser masses, however, significant fractions of mass and energy are radiated away - the smaller the mass, the greater the power. This leads to a runaway process and to a final, gigantic flash of energy in which the black hole evaporates." Not sure how much energy would be released in the final moments, but I know one theory about gamma-ray bursts that are sometimes detected is that they are the signatures of small "primordial black holes" created in the big bang which are just evaporating now. See this paper on the subject, which is discussed in this New Scientist article.

Last edited by a moderator: May 2, 2017
3. Aug 8, 2005

### jimw

Thanks, Jesse. As indicated, I'm not well-versed in physics and expected others had thought about this and reached conclusions. I didn't know there were different densities of black holes. So, would an evaporating hole become less dense and/or larger? (and I hope Hawking would forgive my typo)

4. Aug 8, 2005

### JesseM

No, as you might expect from our intuitive notion of evaporation, an evaporating black hole keeps shrinking down until it disappears. The density is increasing as this happens, but the total mass of the black hole is shrinking (again, because the Schwarzschild formula says that the mass is proportional to the radius).

5. Aug 10, 2005

### Chronos

According to the most popular current models, a black hole could keep evaporating until it reached a Planck mass size [~E-08 kg], then go 'poof'. That would still be a pretty decent 'poof', but not spectacular [an e=mc^2 thing]. Of course there are other candidate models that predict a more [or less] satisfying conclusion. I'm a little shaky on the density thing JesseM mentioned. I don't think it changes. The spacetime curvature as you near the Swarzchild radius makes it very difficult to quantify density. According to the usual Einstein solutions, the singularity itself is generally considered to be infinitely dense. Pretty hard to get more dense than that.

6. Jan 1, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

Yes, makes good sense. There is a threshold of mass wherein a dying star becomes either a neutron star or a black hole. If an evaporating black hole loses enough mass to breach this threshold, the "Strong Atomic Force" would kick in and there would be some type of an explosion. Nothing like a super nova, but nevertheless an explosion. I do not believe black holes evaporate into nothing. This is based on my good understanding of the 4 basic forces of physics: electromagnatism, which is extinguished when a small star becomes a white dwarf, leaving the other 3 remaining; the weak atomic force, which is extinguished when a larger dying star becomes a neutron star, leaving the other 2 remaining; the strong atomic force, which is extinguished when a larger dying star becomes a black hole, leaving only gravity remaining. This determination of what becomes of a dying star is based on the mass involved. Therefore, when a black hole loses sufficient mass, the strong atomic force might come back into play.

:)

7. Jan 1, 2010

### twofish-quant

Re: Do black holes "evaporate" or go "bang"?

I think this is confusing a lot of things.

First of all, one of the things that Hawking figured out is that the larger the black hole the more time it takes to evaporate. In the case of star-sized black holes, the amount of energy that the evaporating black hole produces is very, very small, and you aren't expecting those black holes to do anything over the many many times lifespan of the universe. For you to see a black hole evaporate now, it has to be a tiny black hole. However, no one knows how to form tiny black holes or even if they exist at all.

The threshold at which a star whether becomes a neutron star or a black hole is very unclear since we don't know a lot about this process. In particular, it's not know under what conditions you form a black hole directly and under want conditions you end up with an explosion and then a black hole.

Ummmm.. This is very different from what I learned when I was doing my Ph.D. What keeps things from collapsing isn't a force so much as the Pauli exclusion principle.

8. Jan 1, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

Yes, when talking about black holes, we are talking about times of eternities. Still it's fascinating to understand what we can and to seek to understand more. Happy New Year.

9. Jan 1, 2010

### qraal

Re: Do black holes "evaporate" or go "bang"?

There are no particles in a standard Black Hole so there is no strong-force working against the gravity.
The time span of evaporation, t, is the mass divided by the present mass-loss rate, then divided by 3. i.e. t = M/3.(dM/dt)

The mass loss rate is proportional to the inverse square of the mass. For example a 200,000 ton black hole is evaporating at 0.1 kg/s. Combining these facts tells us that the remaining 229 tons evaporates in 1 second. That's a 4.92 million megaton TNT equivalent explosion.

All the particle identities are merged in the Singularity in standard Black Hole theory so there is no strong force, no colour charge, left to cause such a re-expansion. You can make a theory in which such things are possible, but you'd have to explain how.

And the forces aren't "extinguished", they're overwhelmed. Each stage of collapse produces some quantum-powered opposition to the collapse, as you noted - but that's unstable for large masses. Because pressure is "energy divided by volume" it contributes to a collapsing mass's overall gravitation, thus increasing the amount of squeezing/pressure driving up the gravitation even more... in an 'endless' positive feedback loop that crushes the mass into a point. But that's in classical general relativity which has infinitely small sizes - we don't know if quantum space-time only allows finite volumes or not. Some theories say 'yes', others are less clear.

10. Jan 2, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

Isn't the evaporation time of a black hole is proportional to the cube of its mass?

There's what we KNOW about black holes. There's mathematics, the perfect language. There are theories utilizing mathematics to try to explain the universe, but always with missing links.

Black holes spin rapidly within their accretion disk. As they pull in more matter, they spin faster. MAYBE there's some limit in the universe, just as there are with collapsing stars.. Maybe there's some limit wherein gravity, the sole remaining force of the 4, ceases to exist for a 'split second'. What would you get? If we're talking about quasars, maybe all the matter would spin out into a brand new galaxy.

Do you think black holes are an irreversible state? All matters in the universe tend toward balance, from chaos. It's like the universe playing dice within certain laws, constants, ranges, etc.

I don't believe galaxies are formed like stars or planets by coagulating matter. But by their shapes, especially the spirals, and the fact the the outer arms go faster then the inner arms, so that the entire disk of the galaxy moves together.. I believe they are a reversal of the super massive black hole state.

Black holes contain immense potential energy.. pure matter, no particles, no strong force ONLY mass, gravity and MOVEMENT. They are super hot, super dense, and spinning very rapidly, as they travel thru space, yet containing no space within it.. solid matter.

What becomes of the universe? Does it fail to entropy, or is there some impact, some event, some limit.. wherein gravity ceases to exist..... at which point matter would be released, and all the forces would come back into play in a super CHAOS within the structure of the physics of our universe?

I'm talking along the order of galaxies... rather than The Big Bang. That's another discussion ;)

11. Jan 2, 2010

### sylas

Re: Do black holes "evaporate" or go "bang"?

Yes... given some assumptions such as no mass being absorbed, not even the cosmic background radiation; and the usual assumptions about Hawking radiation. Wikipedia has some useful equations at Hawking radiation.

The relation is
$$t_{ev} = \frac{5120 \pi G^2}{\hbar c^4} M^3 \approx 8.4\times 10^{-17} M^3$$​

Near the end of its life, a small black hole goes bang; the evaporation will release an enormous amount of energy in a very short period of time. For any black hole, we can calculate its temperature, its lifetime, its total energy, and its power output. For a black hole in empty space, soaking up the cosmic background radiation, it will be losing mass only when the temperature is higher than 2.726 K, which is the temperature of the background.

For example, a black hole weighing about a kilogram has a lifetime of about 84 attoseconds (0.000084 picoseconds) and releases as much energy as a 21.5 Megaton thermonuclear bomb. That qualifies as a "bang".

Here is a list of some different masses for black holes; with their total energy content, lifetime, instantaneous power output and characteristic temperature.

$$\begin{array}{l|llll|l} \text{Mass (kg)} & \text{Lifetime (s)} & \text{Power (W)} & \text{Energy (J)} & \text{Temperature (K)} \\ M & \frac{5120 \pi G^2}{\hbar c^4} M^3 & \frac{\hbar c^6}{15360 \pi G^2} M^{-2} & M c^2 & \frac{\hbar c^3}{8 \pi G k_b} M^{-1} \\ & 8.4 \times 10^{-17} M^3 & 3.56\times 10^{32} M^{-2} & 8.99 \times 10^{16} M & 1.23 \times 10^{23} M^{-1} \\ \hline 6\times 10^{-4} & 2\times 10^{-26} & 9.7\times 10^{38} & 5.44 \times 10^{13} & 2 \times 10^{26} & \text{= Hiroshima bomb} \\ 1 & 8.4 \times 10^{-17} & 3.56\times 10^{32} & 9 \times 10^{16} & 1.23 \times 10^{23} & \text{= 21.5 Megaton thermonuclear bomb} \\ 944 & 7.1 \times 10^{-8} & 4 \times 10^{26} & 8.5 \times 10^{19} & 1.3 \times 10^{20} & \text{= same power as Sun} \\ 2.3 \times 10^{5} & 1 & 6.84 \times 10^{21} & 2 \times 10^{22} & 5.4 \times 10^{17} & \text{= 1 second lifetime} \\ 7.2 \times 10^{7} & 3.16 \times 10^{7} & 6.85 \times 10^{16} & 6.5 \times 10^{24} & 1.7 \times 10^{15} & \text{= 1 year lifetime} \\ 1.7 \times 10^{11} & 4.1 \times 10^{17} & 1.24 \times 10^{10} & 1.5 \times 10^{28} & 7.24 \times 10^{11} & \text{= lifetime is age of universe} \\ 4.5 \times 10^{22} & 7.67 \times 10^{51} & 1.76 \times 10^{-13} & 4 \times 10^{39} & 2.7255 & \text{= temperature of cosmic background} \\ 6 \times 10^{24} & 1.8 \times 10^{58} & 1 \times 10^{-17} & 5.37 \times 10^{41} & 2\times 10^{-2} & \text{= mass of the Earth} \\ 2 \times 10^{30} & 6.73 \times 10^{74} & 8.9 \times 10^{-29} & 1.8 \times 10^{47} & 6 \times 10^{-8} & \text{= mass of the Sun} \\ 8 \times 10^{36} & 4.3 \times 10^{94} & 5.6 \times 10^{-42} & 7.2 \times 10^{53} & 1.5 \times 10^{-14} & \text{= Milky Way's supermassive BH} \end{array}$$

I can't believe I just did that. -- Sylas

Last edited: Jan 2, 2010
12. Jan 2, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

And thank you for discussing pressure. Actually, given the masses of the stars that fall into the 3 specific ranges, white dwarf, neutron star, or black hole.. the force of the collapse itself exerts a huge amount of pressure.

So if you have a neutron star taking in the material of a binary star (which is not uncommon), you are increasing the mass of the neutron star, but there is not the force of pressures involved with an implosion.

But it may be possible for a neutron star to gain a LOT of mass and then become unstable. This would be due to the pressures of gravity alone, opposing the Strong Atomic force, which keeps the neutrons intact.

Maybe this is what magnetars are.. They are rare, and are the most magnetic objects in the universe, and they are neutron stars. Maybe they are neutron stars.. going black.

As for the converse, a black hole evaporating into something unstable enough for the other forces to overcome the gravity.. I think this would be much less common. I was asserting an alternative possibility, as I don't believe black holes evaporate away into nothing.

If a black hole were to evaporate down to an unstable state, such that the reduced pressures of gravity could no longer overtake the other forces, there would be an explosion.. not exactly a neutron star as a result :) And there are random flashes throughout this galaxy that scientists cannot explain. ;)

Thanks for an interesting discussion!

Last edited: Jan 2, 2010
13. Jan 2, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

Thank You!

14. Jan 2, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

Have we defined the smallest possible black hole?

I don't believe black holes can be tiny singularities.. or that they can be created in a particle accelerator. They contain mass, they have a size & shape, they possess gravity. They are more than just a "point".

The smaller you get when observing matter, down to atoms and subatomic particles, the less significant the force of gravity becomes. It is actually the least of the forces in the realm of quantum particles.

Since black holes by definition possess only gravity in defining what they are...... we can never create a black hole "singularity" in an accelerator. It just makes sense to me.

15. Jan 2, 2010

### sylas

Re: Do black holes "evaporate" or go "bang"?

The reference to "singularity" is simply an indication that classical physics (GR) breaks down. The "size" of a black hole is usually a reference to the event horizon. But we can still describe reasonably well with classical physics what goes on inside a black hole... up until you get to the center, which is the "singularity"; a point where density diverges to infinite.

To really describe what goes on inside a black hole, where classical physics diverges in a singularity, we'll need to have a theory that combines quantum physics and gravity.

Be that as it may, I don't see any reason in principle to say that a black hole could not be made by a particle accelerator. The problem is that it would take one heck of a lot of energy, and even then any hole would be extremely unstable, because it is so small. It would evaporate almost immediately.

I don't even see how you make that association or inference.

But in any case, a black hole has mass, charge, and spin (angular momentum); so there are three defining properties for a black hole.

Cheers -- sylas

PS. I don't know how reliable this is, but the wikipedia article suggests that Planck mass is a lower limit for a black hole; below that general relativity breaks down completely. This mass is around 2x10-8 kilograms, smaller than any of the holes in my table.

16. Jan 2, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

I was suggesting that a significant amount of mass would be required to initiate a black hole. However, since e = m c squared, then with a sufficient amount of energy, I suppose it might be possible for humans to create a small black hole. But, it would be a LOT of energy, maybe an infinite amount.. and does the charge of a black hole enable magnetic suspension within a partical accelerator? Maybe my assertion about a minimim amount of mass required, is wrong, but I still don't think we can ever do it.

Another thing I find very interesting in the universe, is if you have a photon from a star traveling, say.. East. And in the opposite direction a photon is traveling due west. then the space traveled between the 2 photons is equivalent to twice the speed of light. Does this create a straight-line red shift from the perspective of either photon?

And, would it be true that if 2 galaxies were traveling away from each other such that the net distance growing between them was say exactly the speed of light, then would the light seen from either galaxy of the other, never change? In other words, as they became say 10 billion light years away from each other, they wouldn't necessarily be seeing each other as they were 10 billion light years ago, would they? :)

17. Jan 3, 2010

### sylas

Re: Do black holes "evaporate" or go "bang"?

We are diverging from topic somewhat. It takes a lot of energy to make a black hole; even a small one... but not infinite. There's no such thing as infinite energy; this is just saying you can't make small black holes at all, and there's no reason to claim that.

The exact amount of energy required for a very small black hole is unclear; it would depend on the physics of both relativity and quantum physics and we don't have a complete theory for that. However, any such black hole would be unstable and vanish almost as soon as it was made. The Planck mass (21.8 μg, or 1.22*1016 TeV) is very large by comparison with particles or available energies in an accelerator (The LHC has got up to about 1 TeV, and hopes to get up to as much as 7 TeV). Any black hole made in an accelerator collision would need to be much smaller than planck mass, and we really don't have a good handle on the physics of that scale. In some theories, involving additional dimensions at small scales, it might be possible to make black holes at the TeV scale, which means that it could be possible with the LHC. See Theoretical survey of tidal-charged black holes at the LHC (arXiv:0911.1884); but they would be far too small to be any danger.

As for the points on speed of light; when two photons approach each other, the distance between them decreases at twice lightspeed, for any observer, but nothing is traveling at that speed. For galaxies at large separations, the notion of distance itself becomes ambiguous. This really should be an FAQ... it has been discussed in various threads but I can't pick a good one quickly. But basically, we can see galaxies that have a "proper" recession velocity greater than light speed and the details of why belongs in another thread.

Cheers -- sylas

18. Jan 3, 2010

### gawd.iz.life

Re: Do black holes "evaporate" or go "bang"?

I have thought a lot about these things. I have a passion for physics and cosmology in particular. I will look for other threads as things come up. For instance, I've heard of neutron star quakes and neutron stars having a crust.. and there is some space within a neutron star so that is possible. But black holes are solid all the way thru. So, when they rotate, the outer equator would go faster than the inner core, and of course the center would be gravity-less. For blazars to shoot out jets, from incoming matter at the accretion disk, at near the speed of light from its poles, that thing has to be rotating VERY fast. What would happen if the rotation of the black hole DID reach the speed of light? Maybe THAT's what cancels out gravity for a "split second", with the solid black hole would "unwind" all of its matter outward, in a massive Big Bang, forming a beautiful galaxy, where the outer arm is spinning faster then the inner, just as its solid source, the super massive black hole. I believe this is how galaxies are formed. But I've been away from the math for a long time (I have 152 credits as a math major)....... so I cannot discuss this in terms of mathematics at this time, but I would love to. As for The Big Bang....... I have no idea. I can't comprehend all the mass in the universe altogether at one point. I'm still trying to understand galaxies :)

19. Jan 3, 2010

### DiamondGeezer

Re: Do black holes "evaporate" or go "bang"?

Unfortunately the volume of a Schwarzschild Black Hole is zero using Schwarzschild coordinates, infinite if using Kruskal Szekeres coordinates (but if you include the event horizon the volume is [zero times infinity] which could be anything).

This makes calculating the density of a black hole rather difficult.

But not to worry, because in 30 minutes George Jones will lock the thread saving the result for "pedagogical reasons", so no need to worry about replying. I certainly won't.

Ref: "Volume of a Black Hole" Brandon S. DiNunno, Richard A. Matzner Gen Relativ Gravit (2010) 42:63–76 DOI 10.1007/s10714-009-0814-x Link: http://www.springerlink.com/content/dl8mu550u7736567/

20. Jan 3, 2010

### twofish-quant

Re: Do black holes "evaporate" or go "bang"?

No they haven't. If you look at an intro astronomy text book, it makes it look like we know a lot more than we really do. The separation between a white dwarf and a neutron star is pretty well understood, but the separation mass between a neutron star and a black hole, and what happens at the separation mass is very, very poorly understood.