Author Topic: What happens when a black hole dies?  (Read 5029 times)

Offline bn

  • Titanium Physicist
  • Administrator
  • Godzilla!!!
  • *****
  • Posts: 1065
  • Karma: +1/-0
  • Compressing Hearts, Super Robo Style
    • View Profile
    • The Titanium Physicists Podcast
What happens when a black hole dies?
« on: January 09, 2013, 04:07:17 PM »
Hi so.
the death of a black hole is a complicated thing. and whether a black hole dies, and the details of it, will depend on how complicated/quantum mechanical the theory is. there are three levels of quantum complexity.
  • general relativity (no quantum matter)
  • matter with quantum properties in a classical general relativity context
  • quantum gravity

the deal is, I'm sure you have heard, that quantum mechanics and einstein's theory of general relativity don't play well together.

They are not friends at all.

Einstein's theory is a classical one (no quantum matter) but it's one where "the curvature of spacetime (gravity) tells matter how to move, and the motion of matter tells spacetime how to bend".

because of this, your hands are kind of tied if you want to introduce quantum mechanical matter. because of it's quantum nature, we don't know exactly how it bends spacetime.

but. what you can do is make models where the quantum mechanical matter doesn't really weigh enough to bend the spacetime, and ask "what effect does the curvature of spacetime have on the quantum matter?" (so, it's not a *proper* gravitational model, because we assume that the quantum matter has no gravitational effect).

if you put a quantum field around a black hole, you find something strange. If you drop a particle detector (like a geiger counter) into a black hole and it might say "there is no radiation". but If you take another particle detector and hold it at a constant radius (holding it against the pull of gravity), it will say "there is lots of radiation". this radiation is called Hawking Radiation.  there is a related type of radiation called "Unruh Radiation" which is seen by accelerating spaceships even in spacetimes with no curvature.

anyway. Hawking has a good explanation for what's happening. quantum mechanics, imaginary particle-antiparticle pairs are always popping in and out of existence. If this happens near an event horizon, one of the particles can fall into the black hole, and the other will hang out outside the black hole: giving us a bath of radiation.

In hawking's explanation, the energy used to create the particle that doesn't get swallowed ends up being subtracted from the black hole.

so is the radiation "real"? is it somehow connected to the matter that fell into the black hole? does the black hole actually lose mass as a result of hawking radiation?

no one knows the answers to these questions. obviously, the realness of hawking radiation depends on how tongue-in-cheek you are willing to be with the whole "the quantum matter doesn't gravitate" argument we required to start the calculation. It is a field of active research, and you might hear people talking about firewalls. this is what they are discussing.

So. one question we might want the answer to is "how bright is the hawking radiation/how intense is the energy?" and the answer is that it depends on how small the black hole is. the smallest black holes radiate most strongly.

So really big black holes (like the ones at the center of the galaxy) are "stable", in that they don't radiate very much hawking radiation. Really small black holes (like, if one was made by CERN) are "unstable", in that we would expect them to radiate away their own mass really quickly using this hawking radiation mechanism.

so what's the truth? I'm afraid that until we have a good theory of quantum gravity, we will never know exactly how the emission of quantum particles affects the mass of a black hole :(




Titanium Physicists has a pro-bee-analogy agenda. That's certainly no secret.

Offline Ed Lolington

  • Miocene Terror Bird
  • *******
  • Posts: 241
  • Karma: +0/-0
  • Honorary adjudicator, daytime tweeter.
    • View Profile
    • www.lolington.com
Re: What happens when a black hole dies?
« Reply #1 on: January 09, 2013, 08:10:07 PM »
So. one question we might want the answer to is "how bright is the hawking radiation/how intense is the energy?" and the answer is that it depends on how small the black hole is. the smallest black holes radiate most strongly.

So really big black holes (like the ones at the center of the galaxy) are "stable", in that they don't radiate very much hawking radiation. Really small black holes (like, if one was made by CERN) are "unstable", in that we would expect them to radiate away their own mass really quickly using this hawking radiation mechanism.

I've never really understood how you can have a "small" black hole. Is it less massive than a regular black hole? If it's less massive then what makes it a black hole?

Offline Lynx Cat

  • Miocene Terror Bird
  • *******
  • Posts: 211
  • Karma: +0/-0
    • View Profile
    • Worldline Collapse
Re: What happens when a black hole dies?
« Reply #2 on: January 10, 2013, 04:56:24 AM »
Is the fact that Hawking radiation is stronger for smaller black holes related to a square/cube ratio thing? As in, Hawking radiation is directly proportional to the size of the event horizon (a 2D thing) and the total energy contained in a black hole is directly proportional to its volume (a 3D thing), so the radiation is proportional to the square of the black hole's radius and the energy is proportional to the cube of the same radius, and thus the smaller the radius, the bigger the radiation will be relative to the energy content?

And for Ed's question, I'd think that what makes a black hole what it is is its energy density (how much stuff is packed together in how small a space), not necessarily its total amount of matter/energy. Am I right?
Did I do, O CROM, did I as I said Id do? Good! I did.

Offline bn

  • Titanium Physicist
  • Administrator
  • Godzilla!!!
  • *****
  • Posts: 1065
  • Karma: +1/-0
  • Compressing Hearts, Super Robo Style
    • View Profile
    • The Titanium Physicists Podcast
Re: What happens when a black hole dies?
« Reply #3 on: January 10, 2013, 10:12:59 AM »

I've never really understood how you can have a "small" black hole. Is it less massive than a regular black hole? If it's less massive then what makes it a black hole?

The equations for the geometry of the black hole have an undefined mass parameter. In other words, the mathematics accommodates the existence of ANY SIZED black hole. they can be really really heavy. or the mass of an atom.

the geometric "size" of a black hole is usually given in terms of the Schwarzschild radius: the radius of the event horizon. It's proportional to the mass.

thus, a really small mass black hole will have a really small radius.
Titanium Physicists has a pro-bee-analogy agenda. That's certainly no secret.

Offline bn

  • Titanium Physicist
  • Administrator
  • Godzilla!!!
  • *****
  • Posts: 1065
  • Karma: +1/-0
  • Compressing Hearts, Super Robo Style
    • View Profile
    • The Titanium Physicists Podcast
Re: What happens when a black hole dies?
« Reply #4 on: January 10, 2013, 11:14:20 AM »
Is the fact that Hawking radiation is stronger for smaller black holes related to a square/cube ratio thing? As in, Hawking radiation is directly proportional to the size of the event horizon (a 2D thing) and the total energy contained in a black hole is directly proportional to its volume (a 3D thing), so the radiation is proportional to the square of the black hole's radius and the energy is proportional to the cube of the same radius, and thus the smaller the radius, the bigger the radiation will be relative to the energy content?

And for Ed's question, I'd think that what makes a black hole what it is is its energy density (how much stuff is packed together in how small a space), not necessarily its total amount of matter/energy. Am I right?

nooo. not really. not like.. what was it... beta decay in really heavy atoms?

black holes don't really have an energy density. even inside of their event horizons, the mathematics allows there to be no material. In fact, black hole geometries are vacuum. there is no matter anywhere in the spacetime. just a big ugly hole.

that said. there are mysteries about the whole issue of "black hole thermodynamics", which is what this area of study is called.

the mathematics of black hole growth describe quantities which are kind of analogous to the quantities we deal with in thermodynamics, like the temperature and entropy.

The "temperature" depends on the surface gravity of the black hole.

the "entropy" of a black hole depends on the area of the event horizon surrounding it.

here's the thing. when you factor in hawking radiation; the radiation that comes off of the black hole depends on it's "temperature" in a similar way that the radiation coming out of a furnace would depend on it's temperature.

so then everyone goes "oh wow. instead of being a clever metaphor, maybe these black hole thermodynamics are real actual temperatures and entropies."

but here's the mystery.
the entropy of the black hole depends on the surface area of the black hole,
whereas, the entropy of a box of gas depends on the volume of the box.
 
people have been speculating about what this means for decades.
Titanium Physicists has a pro-bee-analogy agenda. That's certainly no secret.

Offline Lynx Cat

  • Miocene Terror Bird
  • *******
  • Posts: 211
  • Karma: +0/-0
    • View Profile
    • Worldline Collapse
Re: What happens when a black hole dies?
« Reply #5 on: January 10, 2013, 12:10:43 PM »
Whoa, so black holes are a lot more complicated than I initially thought... Cool :D
Did I do, O CROM, did I as I said Id do? Good! I did.

Offline bn

  • Titanium Physicist
  • Administrator
  • Godzilla!!!
  • *****
  • Posts: 1065
  • Karma: +1/-0
  • Compressing Hearts, Super Robo Style
    • View Profile
    • The Titanium Physicists Podcast
Re: What happens when a black hole dies?
« Reply #6 on: January 10, 2013, 12:58:19 PM »
yep. they're a mess.
Titanium Physicists has a pro-bee-analogy agenda. That's certainly no secret.

Offline Random Number

  • Little Puffin
  • **
  • Posts: 7
  • Karma: +0/-0
  • Oxymoron
    • View Profile
Re: What happens when a black hole dies?
« Reply #7 on: March 25, 2013, 01:47:42 AM »
So I have been wondering about this Hawking radiation.

Do we know it exists?

Or dose it just make enough sense to assume that it dose?

And what makes only the positrons "fall" into the black hole?
If it where 50/50 I would assume this mechanism for mass loss would not work.

This Hawking radiation assumes that the Dirac sea is the same inside the event horizon?
So the positron would hit an electron and the mass particle things become something else?
« Last Edit: March 25, 2013, 02:14:09 AM by Random Number »
Mr. Coupon  on Steam
Bad Ideas    on League of Legends

Offline bn

  • Titanium Physicist
  • Administrator
  • Godzilla!!!
  • *****
  • Posts: 1065
  • Karma: +1/-0
  • Compressing Hearts, Super Robo Style
    • View Profile
    • The Titanium Physicists Podcast
Re: What happens when a black hole dies?
« Reply #8 on: March 25, 2013, 05:53:25 AM »
good question.

sooo. we think that hawking radiation exists for a reason which is different than the whole "a positron falls into the black hole" explanation.

we get into it a little in one of the black hole episodes. I think it was the one with alasdair stuart.

it kind of has to do with the definition of a vacuum.
the vacuum is like... "when the quantum field doesn't have any particles in it".
which is fine quantum mechanically, but when you try to mix it up with general relativity,
whether or not you have particles in your quantum field depends on how you are moving relative the the quantum field.

so the moral of the story is that if you are falling into a black hole, you will see a vacuum, but if you are near a black hole and not falling into it, you will see particles. and that's what hawking radiation is.

specifically, if everyone who is free-falling sees a vacuum quantum field, people who are accelerating will observe the same quantum field as having particles in it.
Titanium Physicists has a pro-bee-analogy agenda. That's certainly no secret.

Offline Random Number

  • Little Puffin
  • **
  • Posts: 7
  • Karma: +0/-0
  • Oxymoron
    • View Profile
Re: What happens when a black hole dies?
« Reply #9 on: March 25, 2013, 01:28:48 PM »
Hmm, well this explains my misunderstanding and presents a new problem for me to try and understand.

So I will need to now figure out if my understanding of particles accelerating is correct before I proceed with more questions.

As I do not wish to inconvenience others with all my questions in one place I will try and keep them tied to episodes.

Continued here... http://www.brachiolopemedia.com/forum/index.php/topic,386.0.html
Mr. Coupon  on Steam
Bad Ideas    on League of Legends