Are Black Holes Necessarily Spherical?

[Dorfl]

If two black holes were orbiting each other at a very close distance, would they still be spherical, or would the event horizons become more drop-shaped, just like ordinary binary stars do?

[Soapy Sam]

The one in my washing machine seems to be dustbin - shaped.
Or at least sock shaped.

[Singularitarian]

Yes, the are necesserily sphrical. Always.

[Wudang]

No they are not spherical if they have spin
Amy Barger:
"If we could 'see' black holes, they would be of two different types," Barger says. "One type would have the symmetry of a sphere. The other type would have the symmetry of a top. The latter type of black hole possesses the axial-symmetric shape because it has spin."

from http://www.space.com/scienceastronomy/mystery_monday_030901.html

[Dorfl]

Yes, the are necesserily sphrical. Always.

Why is that?

[Dorfl]

No they are not spherical if they have spin
Amy Barger:
"If we could 'see' black holes, they would be of two different types," Barger says. "One type would have the symmetry of a sphere. The other type would have the symmetry of a top. The latter type of black hole possesses the axial-symmetric shape because it has spin."

from http://www.space.com/scienceastronomy/mystery_monday_030901.html


It seems like Wikipedia (http://en.wikipedia.org/wiki/Black_hole) agrees with that:

Rotating black holes have distorted, nonspherical event horizons.


I can't find anything about binary black holes, though.

[Singularitarian]

The reason is due to a uniform gravitational pull, which nothing can escape apart from virtual particles and hypothetical tachyons. The uniform pull does not differ on area part of the surface area of the black hole.

[sol invictus]

Yes, the are necesserily sphrical. Always.

Once nice thing about Sing is you can always rely on him to be wrong.... no, they certainly are not always spherical. Rotating black holes (and all real black holes will be rotating at least a little) are not spherical. Black holes that have just absorbed something are not spherical. Black holes merging are not spherical. Etc.

In general they behave not unlike droplets.

[Dorfl]

The reason is due to a uniform gravitational pull, which nothing can escape apart from virtual particles and hypothetical tachyons. The uniform pull does not differ on area part of the surface area of the black hole.
But in the case of a binary pair the pull would not be uniform, would it?

[Singularitarian]

I had usually spin not to be so effective on the black holes structure, again due to the gravitational strength.

[Singularitarian]

But in the case of a binary pair the pull would not be uniform, would it?

If anything, they would be pulled together uniformly. Objects moving close to black holes are in a state of free fall.

[Dorfl]

I had usually spin not to be so effective on the black holes structure, again due to the gravitational strength.
Do I interpret this correctly as you having thought spin not to have any noticeable effect on the black hole's structure, due to the vastly greater strength of the gravitational force?

That might be true-ish: I don't know if any black hole will rotate enough to differ very much from the spherical in practice. But in the case of a binary pair, won't there be at least a short while, as they spiral in towards each other, when they are very noticeably non-spherical?

[Dorfl]

If anything, they would be pulled together uniformly. Objects moving close to black holes are in a state of free fall.
I'm not sure what you mean by them being "pulled together uniformly". But the important thing isn't how the black holes are being pulled, is it? The question is how other things are affected by the gravitational force from the holes, and I do not think it will decrease uniformly with radial distance in the binary example.

[sol invictus]

That might be true-ish: I don't know if any black hole will rotate enough to differ very much from the spherical in practice.

It's not. There is a limit to how much a black hole with a given mass can spin, called the extremal limit. Near that limit the shape and spacetime structure of the hole is very different from that of a non-rotating one, and it is believed that nearly all astrophysical black holes come close to saturating the limit.

But in the case of a binary pair, won't there be at least a short while, as they spiral in towards each other, when they are very noticeably non-spherical?

Yep - and after they've merged.

[Singularitarian]

You know, black holes can even spin at the speed of light! Black hole spins vary from different star collapses.

Going back to the question, it is possible if they get close enough, they will begin to stretch, as you would expect any body coming close to the event horizon.

[Dragon]

If anything, they would be pulled together uniformly. Objects moving close to black holes are in a state of free fall.No, not uniformly. There will be tidal forces.

[Singularitarian]

I just mentioned them.

[Dorfl]

Once nice thing about Sing is you can always rely on him to be wrong.... no, they certainly are not always spherical. Rotating black holes (and all real black holes will be rotating at least a little) are not spherical. Black holes that have just absorbed something are not spherical. Black holes merging are not spherical. Etc.

In general they behave not unlike droplets.

I had no idea that their shape would be much different after absorbing something, but now that you say it, I realise that it would have to change slightly. Do they sort of oscillate after absorbing something, or what happens?

[Singularitarian]

Only when they get close together, are the tidal forces taken into account, otherwise, your structure can be uneffected, but the gravitational pull is pulling all the particles in your body at the same rate.

[Dorfl]

It's not. There is a limit to how much a black hole with a given mass can spin, called the extremal limit. Near that limit the shape and spacetime structure of the hole is very different from that of a non-rotating one, and it is believed that nearly all astrophysical black holes come close to saturating the limit.
What happens if you try to make it spin faster?


Yep - and after they've merged.
Cool, what happens then?

[Soapy Sam]

It's not. There is a limit to how much a black hole with a given mass can spin, called the extremal limit. Near that limit the shape and spacetime structure of the hole is very different from that of a non-rotating one, and it is believed that nearly all astrophysical black holes come close to saturating the limit.

Sol- given this sort of mass distorts the spacetime it sits in, can simplistic geometrical terms like "spherical" actually be applied meaningfully at all?

[Dragon]

Only when they get close together, are the tidal forces taken into account, otherwise, your structure can be uneffected, but the gravitational pull is pulling all the particles in your body at the same rate.What do you mean by "rate" in this context?

[shadron]

If you took the Earth and spun it up, you would expect it to go oblate (bulge outwards) along the equator. Similarly, the gravitational fiedl would also become oblate, because the mass in the bulge attracts to itself. The Earth, at the rate it is spinning actually is oblate, and the gravitational field follows along. It is the asymmetry in the field that cases the Earth to slowly exchange rotational momentum with the moon, slowing the Earth's spin and moving the moon's orbit further out.

There is no difference between this model of Earth and a black hole mass. The mass is mysterious only because we cannot see it; there is no reason to suppose it doesn't act in the same way, though the speeds may begin making relativistic effects apparent, just as Mercury orbiting the Sun is not perfectly classical.

This would also apply to binary systems. Picture two sub-black hole stars rotating around each other and how they are distorted by each other's gravitational fields. Black holes would react the same way, barring the relatavistic effects.

[sol invictus]

Do they sort of oscillate after absorbing something, or what happens?

Yeah - they oscillate, damp, and radiate gravity waves while they ring down.

The brightest source for gravity wave detectors is supposed to be black hole mergers.

[Dorfl]

Going back to the question, it is possible if they get close enough, they will begin to stretch, as you would expect any body coming close to the event horizon.

So they do not always have to be spherical?

[sol invictus]

What happens if you try to make it spin faster?

I think what will happen is either the object you try to spin it with will just scatter off the hole without imparting any additional angular momentum, or it will be absorbed and increase the mass enough to "make room" for the additional ang. mom.

Sol- given this sort of mass distorts the spacetime it sits in, can simplistic geometrical terms like "spherical" actually be applied meaningfully at all?

Yes. The horizon of a non-rotating hole is a funny sort of sphere in that its surface area isn't related to its radius in the usual way. But it possesses the defining property of spherical symmetry; namely, it looks the same from all directions.

[Dorfl]

If you took the Earth and spun it up, you would expect it to go oblate (bulge outwards) along the equator. Similarly, the gravitational fiedl would also become oblate, because the mass in the bulge attracts to itself. The Earth, at the rate it is spinning actually is oblate, and the gravitational field follows along. It is the asymmetry in the field that cases the Earth to slowly exchange rotational momentum with the moon, slowing the Earth's spin and moving the moon's orbit further out.

There is no difference between this model of Earth and a black hole mass. The mass is mysterious only because we cannot see it; there is no reason to suppose it doesn't act in the same way, though the speeds may begin making relativistic effects apparent, just as Mercury orbiting the Sun is not perfectly classical.

This would also apply to binary systems. Picture two sub-black hole stars rotating around each other and how they are distorted by each other's gravitational fields. Black holes would react the same way, barring the relatavistic effects.
It being that simple is both cool and disappointing. ;) Thanks! :)

[Dorfl]

I think what will happen is either the object you try to spin it with will just scatter off the hole without imparting any additional angular momentum, or it will be absorbed and increase the mass enough to "make room" for the additional ang. mom.
Is this the "Penrose Effect"?

[Singularitarian]

So they do not always have to be spherical?

From a spin point of view, i guess not, but hey, you learn something new everyday.

From the point of view for two black hole coming relativlely close, you might expect them to pull on each other in such a way that one, or both stretch each other, hence the name, tidal effect.

[Dorfl]

From a spin point of view, i guess not, but hey, you learn something new everyday.

From the point of view for two black hole coming relativlely close, you might expect them to pull on each other in such a way that one, or both stretch each other, hence the name, tidal effect.
Fair enough.

[sol invictus]

Is this the "Penrose Effect"?

Related, yes - although I think you're probably thinking of the reverse process, where you extract some energy (and some angular momentum) from a rotating hole.

[Dorfl]

Related, yes - although I think you're probably thinking of the reverse process, where you extract some energy (and some angular momentum) from a rotating hole.
I thought that was what you meant—a particle absorbs some energy from the Black Hole and therefore gets scattered away from it.

[~enigma~]

From a spin point of view, i guess not, but hey, you learn something new everyday.

From the point of view for two black hole coming relativlely close, you might expect them to pull on each other in such a way that one, or both stretch each other, hence the name, tidal effect.
How could you not know this with your advanced physics education?

[KingMerv00]

How could you not know this with your advanced physics education?

What's funny is nearly every black hole in the universe probably spins so nearly every black hole is non-spherical.

[~enigma~]

What's funny is most, if not all, black holes probably spin so most black holes are not spherical.
True. I am not sure if there are any non-rotating black holes. If there were, it would sure make the math alot simpler.

[geni]

Hmm what does charge do a back hole's shape?

[~enigma~]

Hmm what does charge do a back hole's shape?
Charge can only be very insignificant. Think about it, if the charge were large would it remain so for long?

[KingMerv00]

Charge can only be very insignificant. Think about it, if the charge were large would it remain so for long?

A neutron star is the less massive cousin of a black hole and is composed almost entirely of neutrons. In a neutron star, protons and electrons are squeezed so tightly, they form neutrons and thus lose their charge. I imagine the same thing must happen in a black hole so how could a significant charge exist?

[Wudang]

Am I correct in thinking that non-rotating black holes are just a neat maths solution (makes it easier not handling angular momentum) whereas any existing black hole would statistically have at least some angular momentum as the original star would have some as it formed?
From some reading it looks like a black hole could lose spin by the penrose process but the universe would hit heat death first?
I suspect much of what I recall is hideously outdated.

[KingMerv00]

Am I correct in thinking that non-rotating black holes are just a neat maths solution (makes it easier not handling angular momentum) whereas any existing black hole would statistically have at least some angular momentum as the original star would have some as it formed?

That's what Phil's latest book said.

[~enigma~]

A neutron star is the less massive cousin of a black hole and is composed almost entirely of neutrons. In a neutron star, protons and electrons are squeezed so tightly, they form neutrons and thus lose their charge. I imagine the same thing must happen in a black hole so how could a significant charge exist?
Reread what I wrote. A significant charge can't exist. Not because of any degenerate matter but because a BH would attract oppositly charged particles thus neutralizing any significant charge.

[Monketey Ghost]

Yes, the are necesserily sphrical. Always.

Sweet Fanny Moses, you've got to get away from
1) Making such sweeping statements (especially with regard to your bailiwick, physics; 'always' often applies, and often does not.)

2) Being so confidently wrong.

[KingMerv00]

Reread what I wrote. A significant charge can't exist. Not because of any degenerate matter but because a BH would attract oppositly charged particles thus neutralizing any significant charge.

I understood what you wrote. I was agreeing with you. :D

[~enigma~]

I understood what you wrote. I was agreeing with you. :D
Oh...ok :)

[Dorfl]

Hmm what does charge do to a black hole's shape?
Not much, I think. At least, Wiki's Charged Black Hole article (http://en.wikipedia.org/w/index.php?title=Charged_black_hole&oldid=289076971) does not mention any change. On the other hand, it does somehow add another event horizon inside the normal one. It's explained in this article (http://en.wikipedia.org/w/index.php?title=Reissner–Nordström_metric&oldid=294050852), but I don't claim to understand any of it.

[sol invictus]

Not much, I think. At least, Wiki's Charged Black Hole article (http://en.wikipedia.org/w/index.php?title=Charged_black_hole&oldid=289076971) does not mention any change. On the other hand, it does somehow add another event horizon inside the normal one. It's explained in this article (http://en.wikipedia.org/w/index.php?title=Reissner–Nordström_metric&oldid=294050852), but I don't claim to understand any of it.

Charged, non-rotating black holes are spherical - they have to be, since there's nothing like an angular momentum vector to pick out a special direction - but their spacetime curvature is different, and (like rotating holes) they at least naively seem to have two horizons (I think any real hole actually only has one, but that hasn't been definitely settled either way).

[KingMerv00]

Charged, non-rotating black holes are spherical - they have to be, since there's nothing like an angular momentum vector to pick out a special direction - but their spacetime curvature is different, and (like rotating holes) they at least naively seem to have two horizons (I think any real hole actually only has one, but that hasn't been definitely settled either way).

Two questions Sol, both are born from random curiousity:

1. What exactly do you do for a living? You always come out as the most knowledgable authority in threads like this.

2. What do you think of the theoretical possibility of a naked singularity (http://en.wikipedia.org/wiki/Naked_singularity) (ie a singularity without an event horizon)? I've heard they could possibly form from a rapidly spinning black hole.

[Dorfl]

Charged, non-rotating black holes are spherical - they have to be, since there's nothing like an angular momentum vector to pick out a special direction - but their spacetime curvature is different, and (like rotating holes) they at least naively seem to have two horizons (I think any real hole actually only has one, but that hasn't been definitely settled either way).

Hmm... Do their radius change any if you change the charge?

[Lensman]

Would it be possible to have a toroidal black hole, ie. the event horizon would be a toroid?

I read somewhere (possibly in an Isaac Asimov popular science book) that it would be possible, if it could spin fast enough. I know The Good Doctor was a genius & an excellent researcher, but black hole physics were a little out of his bailiwick.

[KingMerv00]

Would it be possible to have a toroidal black hole, ie. the event horizon would be a toroid?

I don't know the answer but for some reason I think a toroidal black hole would not create an event horizon.

(WARNING WARNING! I may be full of ***** ! Don't take my word for it!)

Edit: From this link (http://en.wikipedia.org/wiki/Naked_singularity#Predicted_formation):

From concepts drawn of rotating black holes (http://en.wikipedia.org/wiki/Rotating_black_hole), it is shown that a singularity, spinning rapidly, can become a ring-shaped object. This results in two event horizons, as well as an ergosphere (http://en.wikipedia.org/wiki/Ergosphere), which draw closer together as the spin of the singularity increases. When the outer and inner event horizons merge, they shrink toward the rotating singularity and eventually expose it to the rest of the universe.

[~enigma~]

Would it be possible to have a toroidal black hole, ie. the event horizon would be a toroid?
The singularity of a rotating BH is a toroid.

[KingMerv00]

The singularity of a rotating BH is a toroid.

So is my link above flat out wrong or does the naked singularity situation only apply to specific toroidal black holes?

[~enigma~]

So is my link above flat out wrong or does the naked singularity situation only apply to specific toroidal black holes?
Your link says rotating BH have toroidal singularities. I was not speaking of naked singularities. But then again, I would never get too comfortable with wikipedia as a scientific source.

[KingMerv00]

Your link says rotating BH have toroidal singularities.

Yes and that the event horizons could cancel out leaving neither one.

But then again, I would never get too comfortable with wikipedia as a scientific source.

I usually check the references and besides, I recall reading about it in "Scientific American" or some similar magazine. I'm not saying it is true, only that it isn't yanked from the ether.

[sol invictus]

1. What exactly do you do for a living? You always come out as the most knowledgable authority in threads like this.

I plead the 5th, as they say in the States.

2. What do you think of the theoretical possibility of a naked singularity (http://en.wikipedia.org/wiki/Naked_singularity) (ie a singularity without an event horizon)? I've heard they could possibly form from a rapidly spinning black hole.

I doubt it - I suspect it's impossible. There's a conjecture to that effect, but it hasn't been proven.

Hmm... Do their radius change any if you change the charge?

"Radius" is a slightly tricky concept in a curved space. But if you define it (as is usually done) as the square root of the area of the horizon divided by 4 pi, then yes - it depends on the charge (with mass held fixed).

Would it be possible to have a toroidal black hole, ie. the event horizon would be a toroid?

I read somewhere (possibly in an Isaac Asimov popular science book) that it would be possible, if it could spin fast enough. I know The Good Doctor was a genius & an excellent researcher, but black hole physics were a little out of his bailiwick.

Not in three spatial dimensions. But it was recently discovered that it's possible in more than three - as are arrangements like "black Saturns" (a ring around a sphere).

The wiki referenced above is talking about the singularity, which is something else.

[Dorfl]

"Radius" is a slightly tricky concept in a curved space. But if you define it (as is usually done) as the square root of the area of the horizon divided by 4 pi, then yes - it depends on the charge (with mass held fixed).

Hmm... It seems like I will need to wait a few years before I know enough maths to understand what that answer really means.

Not in three spatial dimensions. But it was recently discovered that it's possible in more than three - as are arrangements like "black Saturns" (a ring around a sphere).

That sounds bizarrely awesome. Do you have some link where we could read more?

[sol invictus]

Hmm... It seems like I will need to wait a few years before I know enough maths to understand what that answer really means.

It's not so complicated. Imagine drawing a circle on a sphere - a latitude line, say. That latitude line has a length - the circumference of the circle. If you follow a longitude line from the north pole down to the latitude line, you might call that length the radius (you might also call the length from the south pole the radius). But as you'll see if you check, the circumference C does not equal 2 pi R if you define the radius that way. So instead, you might define radius as C/(2 pi).

In general in curved space "radius" can mean different things to different people. A good way to define it for black holes is the square root of the area divided by 4 pi, because that would be the radius in flat space.


That sounds bizarrely awesome. Do you have some link where we could read more?

Enjoy. (http://arxiv.org/abs/hep-th/0701035)

[geni]

So is my link above flat out wrong or does the naked singularity situation only apply to specific toroidal black holes?

My understanding is that it is posible to generate them briefly with highly asymetrical collapses.

[Ziggurat]

Hmm... It seems like I will need to wait a few years before I know enough maths to understand what that answer really means.


It's not actually that hard to understand, but it isn't intuitive to newcomers and it's not taught in highschool geometry.

Suppose I have a flat but stretchable sheet of rubber. I draw a circle on that sheet, and pit a dot at the center. If I ask you what the radius of the circle is, well, you can answer that pretty easily and unambiguously.

But what if I hold the circle down on my table top, grap the spot at the center, and stretch it up? Now what's the radius of the circle? Is it the distance from the circle to the spot I've stretched up, or is it the circumference divided by 2 pi? Either definition is sensible, but they are no longer the same, so one must be careful to specify which it is one is talking about.

In the case of black holes, something a little similar happens in terms of the distortion of space in and around a black hole, though there are additional complications which we don't need to get into here. But the basic idea remains the same: we need to specify what it is we mean by radius since we're not in Euclidean space, and since we can't probe what's happening inside the black hole, a definition based on the surface area is an eminently sensible (though not the only possible) choice.

[Dorfl]

It's not so complicated. Imagine drawing a circle on a sphere - a latitude line, say. That latitude line has a length - the circumference of the circle. If you follow a longitude line from the north pole down to the latitude line, you might call that length the radius (you might also call the length from the south pole the radius). But as you'll see if you check, the circumference C does not equal 2 pi R if you define the radius that way. So instead, you might define radius as C/(2 pi).

In general in curved space "radius" can mean different things to different people. A good way to define it for black holes is the square root of the area divided by 4 pi, because that would be the radius in flat space.

It's not actually that hard to understand, but it isn't intuitive to newcomers and it's not taught in highschool geometry.

Suppose I have a flat but stretchable sheet of rubber. I draw a circle on that sheet, and pit a dot at the center. If I ask you what the radius of the circle is, well, you can answer that pretty easily and unambiguously.

But what if I hold the circle down on my table top, grap the spot at the center, and stretch it up? Now what's the radius of the circle? Is it the distance from the circle to the spot I've stretched up, or is it the circumference divided by 2 pi? Either definition is sensible, but they are no longer the same, so one must be careful to specify which it is one is talking about.

In the case of black holes, something a little similar happens in terms of the distortion of space in and around a black hole, though there are additional complications which we don't need to get into here. But the basic idea remains the same: we need to specify what it is we mean by radius since we're not in Euclidean space, and since we can't probe what's happening inside the black hole, a definition based on the surface area is an eminently sensible (though not the only possible) choice.

Ok. I think I sort of get that. I have some kind of intuitive picture of what it means now.


Enjoy. (http://arxiv.org/abs/hep-th/0701035)
Thanks. :)