A Question Regarding Black Holes

[Mkbul]

Hello people,

I have a question regarding black holes. The way i understand it, black holes form in supernovas, and they occur because the gravitational pull of the stellar remnant is so great that nothing can stop it, and it basically collapses down to a singe point, virtually nothing...

Now, my knowledge of Physics is very limited, since I've only just began studying university level physics, but I've learned that points can't have spin right? Because they are points, rotation itself doesn't make sense. But if that's the case, isn't the conservation of angular momentum broken when a black hole forms? Since the remnant that created the black hole was spinning, as it collapsed, no matter how brief and quick that collapse happens, it should spin faster and faster until it becomes a point and then angular velocity becomes...infinite? Or just none? Don't both cases break the conservation of angular momentum? Or does something else happen that somehow obeys the rule?

I would appreciate an answer to this question, thanks for any replies!

 

[phinds]

Whoever told you they do collapse down to a point misinformed you. They do not.

EDIT: The center of a black hole is called a "singularity" but that does NOT mean "point", it means "the place where our math model breaks down and gives unphysical results, so we don't know what is actually going on". It is believed that if/when we have a theory of quantum gravity the singularity will probably be understood (or at least somewhat understood).

 

[Mkbul]

Whoever told you they do collapse down to a point misinformed you. They do not.

Thanks for the quick reply, i really appreciate it!

If they do not collapse down to a point, then what stops the collapse after it has begun? So the singularity of a black hole actually has a radius? And since it's got a radius, does that mean it's density is not infinite? I have heard too many times that a black hole collapses down to a single point of infinite density, and that's what i also figured, since after the neutrons of a neutron star start to give in, there really isn't something else to stop the collapse...

I want to hear more about this, if you could reply to these questions it would be great! Once again, thanks for the reply.

 

[phinds]

I'd suggest a forum search where you will find threads that go into more detail than I can but we don't know what the singularity is so trying to describe what it is is not presently meaningful.

 

[DaveC426913]

I see his point though. Whether or not we know what the singularity is, we can deduce some things about it.
Its mass, its charge - and its angular momentum.

If we were able to tell how much mass, and with what initial angular momentum, fell into a BH over a given time, and were able to measure its spin afterward, wouldn't we be able to - at least in theory - deduce the final radius of the mass at the centre?

Or am I talking through my hat?

 

[phinds]

That's an interesting argument Dave. You could be right but it seems like we would have heard of such a theory if in fact it worked. Most likely there is something wrong with it, but I certainly can't say what.

 

[Mkbul]

I am glad you can make sense of my post. I did some research in the forums but also in the internet, sadly i couldn't find any older post asking the same question, but i certainly found lots of interesting information about black holes. I was thinking that the singularity was a point, because since there is nothing to stop the collapse it would eventually become dimensionless, so thanks for clearing that up for me on your first post phinds. If anyone has anything more to say on the matter i'd be more than happy to hear it though, since this question still stands, and it's having a negative effect on my sleep at the moment!

Thanks again, Mike.

 

[soothsayer]

If we were able to tell how much mass, and with what initial angular momentum, fell into a BH over a given time, and were able to measure its spin afterward, wouldn't we be able to - at least in theory - deduce the final radius of the mass at the centre?

How would we determine the rotational velocity of a black hole singularity?

 

[soothsayer]

Mkbul, don't be surprised that someone falsely told you that black hole singularities collapse into a dimensionless point. This is a very common description of singularities in popular science. It's one I was taught when I was first learning about black holes/astrophysics.

In classical mechanics and general relativity, there is nothing to stop the collapse of a black hole singularity into an infinitely dense point. When we invoke quantum mechanics, we can come up with a number of alternative theories. Many quantum gravity theories make predictions about the nature of the black hole singularity. One such prediction being the "Fuzzball" that arises from some superstring theories: https://en.wikipedia.org/wiki/Fuzzball_(string_theory)

 

[DaveC426913]

How would we determine the rotational velocity of a black hole singularity?

The first question (for me) is: how do we determine the spin of a black hole in the first place?

 

[newjerseyrunner]

The first question (for me) is: how do we determine the spin of a black hole in the first place?

According to wikipedia, there was an article in 2006 in the Astrophysical Journal, unfortunately, there is no link to it, maybe someone else can find it.

 

[stevebd1]

Hello people,

I have a question regarding black holes. The way i understand it, black holes form in supernovas, and they occur because the gravitational pull of the stellar remnant is so great that nothing can stop it, and it basically collapses down to a singe point, virtually nothing...

Now, my knowledge of Physics is very limited, since I've only just began studying university level physics, but I've learned that points can't have spin right? Because they are points, rotation itself doesn't make sense. But if that's the case, isn't the conservation of angular momentum broken when a black hole forms? Since the remnant that created the black hole was spinning, as it collapsed, no matter how brief and quick that collapse happens, it should spin faster and faster until it becomes a point and then angular velocity becomes...infinite? Or just none? Don't both cases break the conservation of angular momentum? Or does something else happen that somehow obeys the rule?

I would appreciate an answer to this question, thanks for any replies!

In Kerr metric which deals with rotating black holes, you have something called the spin parameter-

$$a=J/mc$$

where a is the spin parameter in metres, J is the angular momentum of the black hole, m is th mass and c is the speed of light. $a$ is often referred to as the coordinate radius of the ring singularity (though technically, r=0 is at the edge of the ring singularity and anything within the RS is considered 'new' space) which is demonstrated best with elliptic coordinates. The equation $a=J/mc$ can be loosely related to the equation for angular momentum for a ring where $J=vmr$ where v is velocity, m is mass and r is radius. In the case of the spin parameter, the equation is rearranged, v=c (the rotational velocity of the RS) and r becomes a.

The bottom two images from the web page below show the Kerr metric in elliptic coordinates (the 'radius' of the ring singularity being $a$)-
http://jila.colorado.edu/~ajsh/insidebh/waterfall.html

The first question (for me) is: how do we determine the spin of a black hole in the first place?

BH spin can be calculated by establishing the location of the inner edge of the accretion disk (the marginally stable orbit or MSO) which is at r=6M for a static black hole and at r=1M for a black hole at maximum spin. The MSO reduces as spin increases due to frame-dragging allowing matter to orbit closer to the BH. The quantity of spin is often defined by a/M (where M=Gm/c², the geometric unit for mass) and can range from 0 for a static black hole up to 1 for a maximal black hole (the max is normally considered to be 0.998). Astrophysicist look for periodic infrared and X-ray emissions from near a BH in order to try and establish the inner edge of the accretion disk and as a result, the spin of the BH. Below are a couple of articles-

Using X-Rays to Measure the Elusive Spin of a Black Hole NY Times

Spinning black_hole is fastest on record New Scientist

 

[Mkbul]

In Kerr metric which deals with rotating black holes, you have something called the spin parameter-

$$a=J/mc$$

where a is the spin parameter in metres, J is the angular momentum of the black hole, m is th mass and c is the speed of light. $a$ is often referred to as the coordinate radius of the ring singularity (though technically, r=0 is at the edge of the ring singularity and anything within the RS is considered 'new' space) which is demonstrated best with elliptic coordinates. The equation $a=J/mc$ can be loosely related to the equation for angular momentum for a ring where $J=vmr$ where v is velocity, m is mass and r is radius. In the case of the spin parameter, the equation is rearranged, v=c (the rotational velocity of the RS) and r becomes a.

The bottom two images from the web page below show the Kerr metric in elliptic coordinates (the 'radius' of the ring singularity being $a$)-
http://jila.colorado.edu/~ajsh/insidebh/waterfall.html
BH spin can be calculated by establishing the location of the inner edge of the accretion disk (the marginally stable orbit or MSO) which is at r=6M for a static black hole and at r=1M for a black hole at maximum spin. The MSO reduces as spin increases due to frame-dragging allowing matter to orbit closer to the BH. The quantity of spin is often defined by a/M (where M=Gm/c², the geometric unit for mass) and can range from 0 for a static black hole up to 1 for a maximal black hole (the max is normally considered to be 0.998). Astrophysicist look for periodic infrared and X-ray emissions from near a BH in order to try and establish the inner edge of the accretion disk and as a result, the spin of the BH. Below are a couple of articles-

Using X-Rays to Measure the Elusive Spin of a Black Hole NY Times

Spinning black_hole is fastest on record New Scientist

Wow, thanks a lot for the very analytic reply. I have never seen this equation before, but to be fair i am new to relativistic mechanics. I'll definitely read these articles too.

 

[soothsayer]

The first question (for me) is: how do we determine the spin of a black hole in the first place?

I think there are ways in theory that you can do it, if you could probe/describe the ergosphere, but from a practical observational standpoint, I know of no way.