I’ll have a regular post up here today, but in the meantime, please read my latest Scientific American guest post: What We Know About Black Holes. I avoid a lot of the thornier theoretical issues surrounding black holes, most of which aren’t yet testable, and instead focus on what we have observed and what any reasonable alternative model would have to explain.
Galileo's Pendulum 
11 responses to “What We Know About Black Holes”
Hi Matthew,
Do you know of any reasonably straightforward algebraic equations that give the radius of a Kerr ring singularity as a function of its mass, energy and/or angular momentum.
Every discussion notes the ring singularity, but I can never find a quick and simple way to approximate its size.
Thanks for any help.
If you go to …www3.amherst.edu/~rloldershaw you can find my email address, and you can respond by email if you prefer.
Rob O
Fractal Cosmology
Here’s a follow-up post that may help answer your question: https://galileospendulum.org/2011/09/02/some-further-notes-on-black-holes/ Let me know if you would like a more mathematical explanation (or some references).
You answer many issues but not the specific question I asked.
What is the radius of the Kerr solution ring singularity?
A point singularity has no radius, but a ring singularity does.
Knowig its size is a critical piece of information.
I am just looking for a ballpark figure.
Thanks
I apologize – that is very much my bad. I rewrote the last two paragraphs to clarify that point, which I realize sounded misleading.
I will send you a mathematical answer to your question via email, since I haven’t had time to write it up yet. Again, apologies.
No problemo!
Especially since no one else who has ever written on Kerr or Kerr-Newman black holes ever states how big the ring is.
And to be clear to other readers, I know the ring is not a torus with a radius. But there must be a distance from one side of the ring to the opposite side.
Maybe no one discusses this question because this is a very difficult question that cannot be answered in a simple manner, for some reason.
Any help you can offer will be much appreciated. Even is the answer is that no one knows.
RLO
Any progress in relating the size of the ring singularity to M or J or the radius of the event horizon?
I haven’t had time to spend on it, with regular blogging and job hunting. It’s still on my agenda, though.
It’s been two weeks. Is the size of the ring singularity unknown?
Is there some expert in General Relativity that you could consult?
You asked me for a favor, and I told you I hadn’t had time to do anything about it yet, but will eventually get to it. As I said before, it’s not in any of the books I have, so I would need to work out the details myself. If you can’t accept that I haven’t had time to work on it (and please note that I’m not being paid to do this or receiving any benefit from it), then you will need to find another expert or work out the calculation yourself.
I imagine the size is known, but is an uninterestingly complicated expression and/or its interpretation is ambiguous in some way.
My apologies: I guess I didn’t say specifically that the answer isn’t in any of my books and that I would have to work it out.
However, I still need to beg your patience on this. I have a lot of commitments, most important of which is finding a job.
Ok, don’t stress.
I’ll ask at sci.physics.research, but I think I have already tried and no one knew there either.
It seems incredibly odd to me that this piece of information is not readily available in many places. It is such a natural question to ask.
If the K and K-N solutions have ring singularities, one of the first questions anybody would ask is: how big/small are they?
If I get any info on this questions, I’ll let you know.
Good luck on the job search.
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PS: Could the stellar mass function be quantized like the atomic mass function. Impossible, right? But just see the evidence discussed at:
http://groups.google.com/group/sci.astro.research/browse_frm/thread/7d6df063296f95d6?hl=en#
It’s a whole new paradigm, my friend!