Seeking proof for the no-hair theorem

September 9, 2014 by Brian Koberlein, One Universe At A Time, One Universe at a Time

According to general relativity, a black hole has three measurable properties: mass, rotation (angular momentum), and charge. That's it. If you know those three things, you know all there is to know about the black hole. If the black hole is interacting with other objects, then the interactions can be much more complicated, but an isolated black hole is just mass, rotation and charge.

In this is known as the no-hair theorem. The basic idea of the no-hair theorem is that the material properties of any object (referred to as "hair" because a physicist named John Wheeler once coined the phrase "a black hole has no hair") become unmeasurable (hence unknowable) as the object collapses into a black hole.

On the surface this seems fairly reasonable. If a neutron star collapses into a black hole, for example, all the neutrons and their interactions become trapped inside the black hole's event horizon when the black hole forms. The same would be true for an object that was lopsided (say with a mountain range on one side). As it collapses into a black hole, any irregularities would be squashed flat as it approaches the black hole limit.

But there are also difficulties with the no-hair theorem. For one, even though it's referred to as a theorem, it has never been proved in general relativity. So it really should be called the no-hair hypothesis. There have been lots of demonstrations that the theorem is reasonable, and computer simulations tend to agree that black holes stabilize to a structure defined by mass, rotation and charge. But none of these reach the level of proof.

Then there is the problem that if a black hole really is just defined by mass, charge and rotation, then it has no temperature, and that means that its entropy is zero. This violates the principles of thermodynamics. Of course when we try to include quantum theory into our black hole description we know that do have a temperature. In Hawking's theory, the temperature of a black hole depends upon its mass, so even a Hawking black hole would be definable by mass, rotation and charge. It's possible that the no-hair theorem is valid even for a quantum black hole.

But there is a more subtle mystery that hides within the no-hair theorem, because it would seem that a black hole is much simpler than other massive objects such as planets, stars and the like. If you think about an object like the Sun, it has a certain chemical composition, and it's giving off light with different wavelengths having varying intensities. There are sunspots, solar flares, convection flows that create granules, and the list goes on. The Sun is a deeply complex object that we have yet to fully understand. And yet, if our Sun were compressed into a black hole, all that complexity would be reduced to mass, rotation and charge. So what happens when a complex object like a star collapses into a black hole? Where does all that complexity go?

In physics we refer to that complexity as the physical information of a system. According to , physical information is never lost, but according to general relativity and the no-hair theorem, physical information that enters a black hole is lost forever. This contradiction is known as the black hole information paradox, or sometimes the firewall paradox. Now you might think that the easy answer is just to presume the no-hair is wrong.

But it's not that simple, and if we started exploring that paradox, things would get a bit hairy.

Explore further: What would it be like to fall into a black hole?

Source:: One Universe at a Time

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13 comments

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eltodesukane
3 / 5 (2) Sep 09, 2014
Black holes are known to have a very high entropy (Bekenstein-Hawking entropy, Bekenstein–Hawking formula).
So the no-hair theorem of general relativity is obviously false.
Jixo
Sep 09, 2014
This comment has been removed by a moderator.
Jixo
Sep 09, 2014
This comment has been removed by a moderator.
saposjoint
3 / 5 (6) Sep 09, 2014
Zephyr, you ignorant slut.
Melchizedek0001
1 / 5 (5) Sep 09, 2014
Who writes this? A scientist or an UFO-creature? Psychological feelings here about physics and blcka holes leave for TV's and Hollywood's mobs. Use strict logical rules and laws plus physics's terms with their strict definitions (as extensive terms).What do you mean by proof? By deduction, reduction or aquintance? Another a science fool searching for "mysteries" like in twin (Relativity) or Schrodinger cat paradox (Quantum Mechanics). Except the existence of evil there is no more mysteries: for an exmaple one must use the axiom of choice that will never be proven to prove other theroems of mathematics and by analogy in other science and philosophy like the existence of the first cause....just a little for now
Aligo
Sep 09, 2014
This comment has been removed by a moderator.
Returners
1 / 5 (4) Sep 09, 2014
Zephyr, you ignorant slut.


I actually agree with him on this.

If you imagine dropping an object from rest relative to the black hole, from various altitudes ranging from equal to the Schwarzchild Radius, to about 4 times such radius, you will find that the point where the object's velocity goes to c, and relative mass would try to go asymptotic changes with respect to it's initial position. What this means is the black hole has an infinite number of "surface radii" and each object which falls into it cannot actually pass that point, and this point is different for every position. The claim that you would not pass the event horizon is only true for objects approaching gravitationally from infinity, and is not true for objects having origins closer than infinity. They fall past the event horizon, but then hit another event horizon which they cannot pass, which is different for each initial distance.

You can actually see this in the schwarzchild radius formula.
Returners
1 / 5 (4) Sep 09, 2014
This phenomenon was described in "Black Holes: A Traveller's Guide" and I think also by Hawking himself on one or more occasions. So from that perspective, Black holes are actually more complicated than ordinary objects.

Now the Schwarzchild radius assumes an initially tangential velocity such that even "c" is not great enough to overcome the light, but if you just imagine dropping an object and it going straight in, from each of those distances, you can integrate to get the v^2 component of work, and then take square root to get velocity (approximately) and this number cannot exceed "c" within relativity, which means the object cannot be accelerated any farther, and time would essentially stop for that object (relativity claim again).

Basically, the slower you are moving, the bigger the event horizon, but that's beside the point. It paradoxically means that some viewers could be inside an event horizon while nevertheless being farther from the center in another viewers' frame.
Aligo
Sep 09, 2014
This comment has been removed by a moderator.
Returners
1.6 / 5 (7) Sep 09, 2014
Oh yeah, my above posts point out another fact. The "Singularity" of "infinity Density" does not actually exist, and it is actually forbidden by Relativity.

Why?

1, matter would need to reach or exceed v = "c" in order to reach the singularity, which we all know the theory forbids in the first place.
2, As mentioned above, objects with different initial distances would have their asymptotes at a different altitude anyway, which means the singularity is impossible (if the universe has a max speed), even 1 above were not true.
Tri-ring
not rated yet Sep 10, 2014
If you think about it the "black hole information paradox" is at question since according to special relativity, energy and mass is interchangeable meaning physical information is "Created" when energy changes to mass so I believe the opposite is also possible.

Does mass always require physical information?
What is mass?
TheGhostofOtto1923
3.7 / 5 (3) Sep 10, 2014
1, matter would need to reach or exceed v = "c" in order to reach the singularity, which we all know the theory forbids in the first place
Indeed doctor of pharmaceutical engineering, if this is true them why did you say only an hour previously
you will find that the point where the object's velocity goes to c
???

Perhaps the evolution of your theory has more to do with the progress of therapeuticals through your system than with systematic exploration and reasoned analysis.
antialias_physorg
5 / 5 (3) Sep 10, 2014
location and velocity? How about history (age)?

How does the location and speed affect the object?
Either is only relative to another observer, so it's not an intrinsic property of the black hole itself.

History is also not a a property that distinguishes one black hole of a certain mass, charge and spin from another with the same mass charge and spin.

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