Seeking proof for the no-hair theorem

September 9, 2014 by Brian Koberlein, 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


Related Stories

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

September 8, 2014

Let's say you decided to ignore some of my previous advice. You've just purchased yourself a space dragon from the Market on the Centauri Ringworld, strapped on your favorite chainmail codpiece and sonic sword and now you're ...

How fast do black holes spin?

February 14, 2014

There is nothing in the Universe more awe inspiring or mysterious than a black hole. Because of their massive gravity and ability to absorb even light, they defy our attempts to understand them. All their secrets hide behind ...

Black holes do not exist as we thought they did

February 14, 2014

On January 24, the journal Nature published an article entitled "There are no black holes." It doesn't take much to spark controversy in the world of physics... But what does this really mean? In a brief article published ...

Can light orbit a black hole?

March 25, 2014

Since black holes are the most powerful gravitational spots in the entire Universe, can they distort light so much that it actually goes into orbit? And what would it look like if you could survive and follow light in this ...

Recommended for you

Bursts of methane may have warmed early Mars

January 24, 2017

The presence of water on ancient Mars is a paradox. There's plenty of geographical evidence that rivers periodically flowed across the planet's surface. Yet in the time period when these waters are supposed to have run—three ...

Gaia turns its eyes to asteroid hunting

January 24, 2017

While best known for its surveys of the stars and mapping the Milky Way in three dimensions, ESA's Gaia has many more strings to its bow. Among them, its contribution to our understanding of the asteroids that litter the ...

Dwarf galaxies shed light on dark matter

January 23, 2017

The first sighting of clustered dwarf galaxies bolsters a leading theory about how big galaxies such as our Milky Way are formed, and how dark matter binds them, researchers said Monday.

One of the brightest distant galaxies known discovered

January 23, 2017

An international team led by researchers from the Instituto de Astrofísica de Canarias (IAC) and the University of La Laguna (ULL) has discovered one of the brightest "non-active" galaxies in the early universe. Finding ...


Adjust slider to filter visible comments by rank

Display comments: newest first

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.
no fate
1 / 5 (10) 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.

Black Holes describe the portion of the brain where logic once existed but has been replaced by 100 year old incorrect dogma, if you suffer from this condition then you also believe that our physcial universe can produce them in space.

"Of course when we try to include quantum theory into our black hole description we know that black holes do have a temperature."

So what part of the equation on the quantum scale demonstrates the precise physical mechanism by which gravity overwhelms all other forces? Reactions on the quantum scale give us all of our classical physics, there is no "quantum gravity". How the hell can you just ignore this as though saying " if you get enough stuff in one spot it happens" is an acceptable explanation? Matter cannot self compress out of our universe.
Sep 09, 2014
This comment has been removed by a moderator.
Sep 09, 2014
This comment has been removed by a moderator.
3 / 5 (6) Sep 09, 2014
Zephyr, you ignorant slut.
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
Sep 09, 2014
This comment has been removed by a moderator.
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.
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.
Sep 09, 2014
This comment has been removed by a moderator.
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.


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.
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?
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.
1 / 5 (2) Sep 10, 2014
One of my pet peeves (among the seething countless hoard) is stupid claims that if you know charge, mass and spin, then you know everything about a black hole. Uh, how about location and velocity? How about history (age)? The event horizon(s) of two merging bhs require more than what this simple claim allows. In point of fact, a black hole is 'located' at a TIME rather than a to speak. Notice how some comments here confuse observers: the observer at 'infinity' (or sufficient distance from bh) is very different than any and all observers falling through the event horizon (leaving this Universe). Describing what the latter observes is Religion, as it is, by definition, not something which is meaningful (in this Universe). You can let me know should it ever become meaningful to you: I'll await your
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.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.