mkline55

2013-Aug-30, 05:26 PM

Is the theoretical maximum spin rate for a black hole limited to the speed at which the event horizon is moving at light speed compared to some distant observer? Why, or why not?

View Full Version : Black hole angular momentum limitations

mkline55

2013-Aug-30, 05:26 PM

Is the theoretical maximum spin rate for a black hole limited to the speed at which the event horizon is moving at light speed compared to some distant observer? Why, or why not?

Strange

2013-Aug-30, 06:37 PM

This has come up a few times before:

A black hole must satisfy the following inequality:

\frac{J^2}{M^2} + Q^2 \leq M^2

Where J is angular momentum (how fast it spins), Q is electric charge and M is the mass of the black hole, in units where G=c=1.

This gives an upper bound on how fast it can spin and its charge.

From this thread: http://cosmoquest.org/forum/showthread.php?123113-How-fast-could-a-black-hole-spin

A black hole must satisfy the following inequality:

\frac{J^2}{M^2} + Q^2 \leq M^2

Where J is angular momentum (how fast it spins), Q is electric charge and M is the mass of the black hole, in units where G=c=1.

This gives an upper bound on how fast it can spin and its charge.

From this thread: http://cosmoquest.org/forum/showthread.php?123113-How-fast-could-a-black-hole-spin

mkline55

2013-Aug-30, 07:04 PM

Thanks. Then an uncharged black hole cannot spin at a speed which would result in the event horizon moving faster than c. That would agree with what I've read regarding the singularity forming a flat disk. It also indicates that the disk could not shrink further unless it lost momentum simultaneously. Is frame dragging the most likely cause of momentum loss?

caveman1917

2013-Aug-30, 07:51 PM

Thanks. Then an uncharged black hole cannot spin at a speed which would result in the event horizon moving faster than c. That would agree with what I've read regarding the singularity forming a flat disk. It also indicates that the disk could not shrink further unless it lost momentum simultaneously. Is frame dragging the most likely cause of momentum loss?

Frame dragging by itself doesn't change the black hole's angular momentum (it's not a literal "dragging" in the sense that there is some sort of resistance at work). The black hole can lose angular momentum by interaction with other objects, and in that sense frame dragging can make the interaction more likely to leave the black hole with less angular momentum than more - but you still need the other object that interacts with it.

Frame dragging by itself doesn't change the black hole's angular momentum (it's not a literal "dragging" in the sense that there is some sort of resistance at work). The black hole can lose angular momentum by interaction with other objects, and in that sense frame dragging can make the interaction more likely to leave the black hole with less angular momentum than more - but you still need the other object that interacts with it.

wd40

2013-Sep-01, 11:12 PM

In his 1994 “Angular Momentum of Cylindrical Systems in General Relativity", Hermann Bondi showed that angular velocities many multiples of c are allowed by General Relativity

http://www.jstor.org/discover/10.2307/52457?uid=3738240&uid=2129&uid=2&uid=70&uid=4&sid=21102599950847

http://www.jstor.org/discover/10.2307/52457?uid=3738240&uid=2129&uid=2&uid=70&uid=4&sid=21102599950847

Hornblower

2013-Sep-01, 11:21 PM

In his 1994 “Angular Momentum of Cylindrical Systems in General Relativity", Hermann Bondi showed that angular velocities many multiples of c are allowed by General Relativity

http://www.jstor.org/discover/10.2307/52457?uid=3738240&uid=2129&uid=2&uid=70&uid=4&sid=21102599950847

Angular velocity does not have the same units as c. Please explain.

http://www.jstor.org/discover/10.2307/52457?uid=3738240&uid=2129&uid=2&uid=70&uid=4&sid=21102599950847

Angular velocity does not have the same units as c. Please explain.

mkline55

2013-Sep-03, 01:06 PM

In his 1994 “Angular Momentum of Cylindrical Systems in General Relativity", Hermann Bondi showed that angular velocities many multiples of c are allowed by General Relativity

http://www.jstor.org/discover/10.2307/52457?uid=3738240&uid=2129&uid=2&uid=70&uid=4&sid=21102599950847

I've read the article, and find the following:

The range of permitted values is ... so that neither tangential velocity exceeds the speed of light.

Although interesting, the author is dealing with hollow cylinders with an infinitely thin, but dense outer shell. No length seems to be implied, nor are any other dimensions provided. What is the connection between math of cylinders and black holes?

http://www.jstor.org/discover/10.2307/52457?uid=3738240&uid=2129&uid=2&uid=70&uid=4&sid=21102599950847

I've read the article, and find the following:

The range of permitted values is ... so that neither tangential velocity exceeds the speed of light.

Although interesting, the author is dealing with hollow cylinders with an infinitely thin, but dense outer shell. No length seems to be implied, nor are any other dimensions provided. What is the connection between math of cylinders and black holes?

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