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An Introduction to Black Hole Thermodynamics

by Greg Bernhardt
Tags: black, hole, introduction, thermodynamics
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Greg Bernhardt
#1
Oct28-03, 12:55 AM
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Black Holes have always ben a controversial affair among Theoretical Astrophysicists. Especially, the Thermodynamics of a Black Hole. It was considered that the entropy of a Black Hole is infinitely large until Stephen Hawking proved that Black Holes are not really Black. They infact Radiate and evaporate... How is this so? What are the laws of Thermodynamics governing this process? Read on...

http://physicspost.com/articles.php?articleId=176
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Unkaspam
#2
Oct28-03, 07:59 PM
P: 42
This is really interesting about black holes. Thank you for posting the article.

It gets confusing when people say that light has no mass but does not escape the gravitational radiation of a black hole. Does the r mass of light present enough mass to be pulled into the black hole? Or is it the warp in space-time that leads light into it?

If electrons can escape the gravitational pull of a black hole by way of virtual pair production then I don't see why light is pulled into the black hole.
Ambitwistor
#3
Oct28-03, 08:07 PM
P: 837
Originally posted by Unkaspam
It gets confusing when people say that light has no mass but does not escape the gravitational radiation of a black hole. Does the r mass of light present enough mass to be pulled into the black hole? Or is it the warp in space-time that leads light into it?
You can look at it from either the perspective of the gravitational influence on particles with relativistic mass-energy, or from the influence of curved spacetime on trajectories. Either way, no object (that travels at less than the speed of light) can escape a black hole.


If electrons can escape the gravitational pull of a black hole by way of virtual pair production then I don't see why light is pulled into the black hole.
Real electrons do not escape a black hole from within the horizon. Neither does light.

Unkaspam
#4
Nov1-03, 12:15 PM
P: 42
An Introduction to Black Hole Thermodynamics

Originally posted by Ambitwistor
[B]Either way, no object (that travels at less than the speed of light) can escape a black hole.
Light travels at the speed of light. Why can't light escape a black hole?


Real electrons do not escape a black hole from within the horizon. .
The article says that black holes evaporate through virtual pair production of electrons that leave the bh's mass. Eventually, no black hole. Therefore, isn't something 'real' escaping the black hole?
Ambitwistor
#5
Nov1-03, 12:24 PM
P: 837
Originally posted by Unkaspam
Light travels at the speed of light. Why can't light escape a black hole?
I should have said, no object (that travels at less than or equal to the speed of light) can escape a black hole.


The article says that black holes evaporate through virtual pair production of electrons that leave the bh's mass. Eventually, no black hole. Therefore, isn't something 'real' escaping the black hole?
No. The real particles that make up the Hawking radiation come from just outside the horizon, not inside it.

(Virtual particles can escape from inside the hole because they can travel faster than light. But we can't observe them.)
Unkaspam
#6
Nov8-03, 05:49 PM
P: 42
Originally posted by Ambitwistor
No. The real particles that make up the Hawking radiation come from just outside the horizon, not inside it.
Yet we see an evaporation of the actual "object", the black hole. How is there any "matter" lost or evaporated from the mass of the black hole if it is only lost from the Hawking radiation just outside the horizon of the bh? (sorry, more questions)

Originally posted by Ambitwistor
(Virtual particles can escape from inside the hole because they can travel faster than light. But we can't observe them.)
If we can't observe virtual particles how do we know they are escaping? Was this hypothesis arrived at through astrophysics calculations?
Ambitwistor
#7
Nov8-03, 05:59 PM
P: 837
Originally posted by Unkaspam
Yet we see an evaporation of the actual "object", the black hole. How is there any "matter" lost or evaporated from the mass of the black hole if it is only lost from the Hawking radiation just outside the horizon of the bh?
The handwavy explanation is that the particles which fall into the hole have negative energy. (I don't know how to describe the non-handwavy explanation.)

No matter is lost from the black hole (which usually contains no matter), but the location of the event horizon changes, and thus the black hole loses mass.


If we can't observe virtual particles how do we know they are escaping?
Well, this is where people get into arguments over whether virtual particles are "really there" or not --- there's a reason why they're called "virtual". In quantum field theory, real, observable physics (such as the ordinary example of the existence of an electric field surrounding a point charge) is described as a "sum" over all possible virtual processes that can happen. Since all we ever observe is the sum of all the processes, it's debatable whether we can say that any single one of them is "really happening". Yet, the prediction you get when you sum over these virtual processes does agree with what is observed in experiments.


Was this hypothesis arrived at through astrophysics calculations?
No, it's standard quantum field theory.
Unkaspam
#8
Nov9-03, 01:25 PM
P: 42
Originally posted by Ambitwistor
No matter is lost from the black hole (which usually contains no matter), but .
If a black hole doesn't contain matter is it because the matter was converted to pure energy during a sun's collapse which led to that sun becoming a black hole? Is the matter of the sun compressed so much that it loses the properties of matter? while retaining the properties of the laws of thermodynamics.

Originally posted by Ambitwistor
the location of the event horizon changes, and thus the black hole loses mass.
Where does the lost mass go? Background radiation? Is the lost mass r-mass, virtual mass or ?
Ambitwistor
#9
Nov9-03, 01:30 PM
P: 837
Originally posted by Unkaspam If a black hole doesn't contain matter is it because the matter was converted to pure energy during a sun's collapse which led to that sun becoming a black hole?
It's because any matter inside the hole very quickly gets crushed out of existence at the singularity.

(Or at least, that's as far as we can tell from general relativity: once something hits the singularity, it ceases to exist as far as GR is concerned. Whether that is actually the case is another matter; GR is expected to break down at high curvatures anyway. Maybe some matter remains in a highly compressed state, and there is no true singularity.)


Where does the lost mass go? Background radiation? Is the lost mass r-mass, virtual mass or ?
The mass lost by the black hole goes into the mass-energy of the Hawking radiation, which is real, not virtual: you could measure it, in principle.
Unkaspam
#10
Nov9-03, 03:56 PM
P: 42
Originally posted by Ambitwistor
It's because any matter inside the hole very quickly gets crushed out of existence at the singularity.

(Or at least, that's as far as we can tell from general relativity: once something hits the singularity, it ceases to exist as far as GR is concerned. Whether that is actually the case is another matter; GR is expected to break down at high curvatures anyway. Maybe some matter remains in a highly compressed state, and there is no true singularity.)



The mass lost by the black hole goes into the mass-energy of the Hawking radiation, which is real, not virtual: you could measure it, in principle.
Thanks Ambitwistor. I'm getting some of this now! If a black hole really is a "hole" then its evaporation would be more like filling in the hole rather than having the hole "evaporate".

Or is it that when the highly compressed state of matter becomes a singularity, it presents a hole in the theory of general relativity or can the mass of singularity still be viewed as a condensed "mass" in relation to other masses such as planets?

One more question, does Hawking radiation have a mass?
Ambitwistor
#11
Nov9-03, 04:16 PM
P: 837
Originally posted by Unkaspam
Thanks Ambitwistor. I'm getting some of this now! If a black hole really is a "hole" then its evaporation would be more like filling in the hole rather than having the hole "evaporate".
I'd rather just say that the horizon and mass of the hole shrinks, than say that the hole is "filled in".


Or is it that when the highly compressed state of matter becomes a singularity, it presents a hole in the theory of general relativity or can the mass of singularity still be viewed as a condensed "mass" in relation to other masses such as planets?
It's not possible to define the mass of the singularity, but the black hole itself has a mass. And yes, a singularity is a "hole" in general relativity; GR fails to make predictions about singularities.


One more question, does Hawking radiation have a mass?
It has mass-energy, like any radiation. If you enclosed some of it in a box, the box would have mass.
jcsd
#12
Nov10-03, 04:36 PM
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Without meaning to be too crtical of Srindlar, there are sevral misleading and inaccurate staements in the article, most notably that the masses given in how a black hole is formed is only the final mass of the black hole/neutron star (the mass of the stars that gave rise to the BH would be signifcvantly larger (<25 solar mass), but this would be thrown off by the star before graviational collapse)and the entropy of black hole is directly proportional to the area of it's event horizon not the square of the area.
muccasen
#13
Jan2-08, 11:33 AM
P: 28
Quote Quote by Unkaspam View Post
This is really interesting about black holes. Thank you for posting the article.

It gets confusing when people say that light has no mass but does not escape the gravitational radiation of a black hole. Does the r mass of light present enough mass to be pulled into the black hole? Or is it the warp in space-time that leads light into it?

If electrons can escape the gravitational pull of a black hole by way of virtual pair production then I don't see why light is pulled into the black hole.
Light has no rest mass. It does have mass in the sense that it has energy and ,as you know e=mc^2. Hence you will note people saying light has mass-energy

Light at but not crossing the event horizon goes around and around the hole. If it crosses the event horizon then it cannot return. The conventional reason is that to do so it would need to reverse time as the future lies toward the singularity {viewed from the outside anyway}.

Electrons,any particle existing outside the event horizon has the possibility of escape 9given enough energy applied to do so or alternatively it can orbit the hole This also applies to light. A Virtual electron is still an electron i.e. if for some reason it avoided cancellation it would continue to exist as an electron
muccasen
#14
Jan2-08, 11:48 AM
P: 28
Quote Quote by Ambitwistor View Post
You can look at it from either the perspective of the gravitational influence on particles with relativistic mass-energy, or from the influence of curved spacetime on trajectories. Either way, no object (that travels at less than the speed of light) can escape a black hole.



Real electrons do not escape a black hole from within the horizon. Neither does light.
No known object can leave a black hole including particles travelling at 'c'. This includes virtual particles. NB the space inside the event horizon is still space and as such has virtual particles, I suggest
muccasen
#15
Jan2-08, 11:59 AM
P: 28
Quote Quote by Unkaspam View Post
Light travels at the speed of light. Why can't light escape a black hole?



The article says that black holes evaporate through virtual pair production of electrons that leave the bh's mass. Eventually, no black hole. Therefore, isn't something 'real' escaping the black hole?
Particles and anti particles both have positive mass. Lets suppose that a virtual pair very close to the event horizon appear and that one of the pair just happens to be headed the right way to avoid crossing the event horizon whilst the other is not and falls in. Ok? Then the infalling particle is anhillated by its matching opposite.... in so doing the matching particle is also eliminated. The black hole is now minus 1 particle. 1 particle less mass. Bear in mind it does not matter whether the particle is positive or negative either would 'weigh', have the same mass.
Handwaving? no better than that, ask SH for better,
muccasen
#16
Jan2-08, 12:02 PM
P: 28
Quote Quote by Ambitwistor View Post
I should have said, no object (that travels at less than or equal to the speed of light) can escape a black hole.



No. The real particles that make up the Hawking radiation come from just outside the horizon, not inside it.

Above agreed

(Virtual particles can escape from inside the hole because they can travel faster than light. But we can't observe them.)
Nah, sorry see above.
muccasen
#17
Jan2-08, 12:13 PM
P: 28
Quote Quote by Ambitwistor View Post
The handwavy explanation is that the particles which fall into the hole have negative energy. (I don't know how to describe the non-handwavy explanation.)

No matter is lost from the black hole (which usually contains no matter), but the location of the event horizon changes, and thus the black hole loses mass.

Sorry m8 this ain't right. A black hole has information observable. It includes it's mass. Mass can be lost via Hawking radiation as described (ish). The higher the black hole mass then the larger the hole and the greater the radius of the event horizon. If/when the hole looses mass the event horizon will change i.e. shrink. Particles falling in do not need negative energy. They just need their opposite from within so that both are eliminated as above



Well, this is where people get into arguments over whether virtual particles are "really there" or not --- there's a reason why they're called "virtual". In quantum field theory, real, observable physics (such as the ordinary example of the existence of an electric field surrounding a point charge) is described as a "sum" over all possible virtual processes that can happen. Since all we ever observe is the sum of all the processes, it's debatable whether we can say that any single one of them is "really happening". Yet, the prediction you get when you sum over these virtual processes does agree with what is observed in experiments.



No, it's standard quantum field theory.
Suggest you review this stuff as it's easy to screw up (I have many times)
muccasen
#18
Jan2-08, 12:19 PM
P: 28
Quote Quote by jcsd View Post
Without meaning to be too crtical of Srindlar, there are sevral misleading and inaccurate staements in the article, most notably that the masses given in how a black hole is formed is only the final mass of the black hole/neutron star (the mass of the stars that gave rise to the BH would be signifcvantly larger (<25 solar mass), but this would be thrown off by the star before graviational collapse)and the entropy of black hole is directly proportional to the area of it's event horizon not the square of the area.
should this be >25 solar masses rather than <25 solar masses


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