I Frame Dragging Around Spinning Black Holes: Implications

[Robert Friz]

TL;DR Summary

The question is whether the spin and extreme gravity of a black hole causes frame dragging to vector the fabric of space itself towards and into the black hole.

Frame dragging around a spinning black hole is generally accepted in cosmology. Does the frame dragging result solely in space-time rotating forever around the black hole, or does frame dragging ultimately result in space-time vectoring towards and into the black hole?

An additional question involves the accretion disk. Does the mass in an accretion disk add to or detract from the rotational frame dragging? Furthermore, since the matter in an accretion disk is moving towards the black hole while rotating around it, does the mass of the accretion disk create a vector for frame dragging space-time towards and ultimately into the black hole?

If either or both frame dragging mechanisms result in moving space-time itself towards and into the black hole, then the street-talk description might be that the black hole is "eating space-time". This has implications...

 

[Ibix]

Does the frame dragging result solely in space-time rotating forever around the black hole, or does frame dragging ultimately result in space-time vectoring towards and into the black hole?

Spacetime doesn't rotate. You have to remember that it's a four dimensional entity - so "space now" is a different slice of spacetime from "space a moment ago". Space a moment ago doesn't change, move, or rotate (how could it?) and nor does space now. But spacetime around a rotating black hole is curved in such a way that inertially moving objects will tend to circle around the black hole.

So no, in short, spacetime is not disappearing into black holes. It isn't a thing that could do - "fabric" of spacetime is a vaguely evocative term that shouldn't be taken at all seriously.

An additional question involves the accretion disk. Does the mass in an accretion disk add to or detract from the rotational frame dragging?

I would expect that the accretion disc does contribute to frame dragging. We have detected the effect from the Earth's rotation, so it seems reasonable that an accretion disc would generate it too, although the effect may well be negligible - I don't know how massive accretion discs are. I have not seen any maths to prove that conjecture, though, and I suspect it would require numerical solutions and be quite time consuming to do. It doesn't change anything about my first two paragraphs.

 

[Robert Friz]

Thank you for your thoughtful reply. As an amateur, I have a very active imagination but no graduate level physics education, which results in going down blind alleys sometimes. Your help was appreciated!

 

[Ibix]

You're welcome.

A former mentor here, Ben Crowell, teaches a non-mathematical course in relativity. The course notes are a book, which can be downloaded free from http://lightandmatter.com/poets/, if you want a look. It's pretty good, and fairly honest about what can be understood without maths.

 

[Robert Friz]

You're welcome.

A former mentor here, Ben Crowell, teaches a non-mathematical course in relativity. The course notes are a book, which can be downloaded free from http://lightandmatter.com/poets/, if you want a look. It's pretty good, and fairly honest about what can be understood without maths.

Ben Crowell's course is indeed quite good. I have delved into it, and while a good deal of the material is familiar, it is presented in one of the most interesting and compelling formats I have encountered. Thanks so much for the reference.

Bob

 

[PeterDonis]

Moderator's note: Moved thread to relativity forum.

 

[romsofia]

I like this page from the Gravity Probe B experiment that describes a lot of the physics around frame dragging, etc:
https://einstein.stanford.edu/SPACETIME/spacetime4.html (note that you should also check out the pages on Netwon's spacetime, Einstein, etc they have a lot of fun info as well!)

 

[Robert Friz]

Yes, the website you mentioned was interesting. GP-B was a fascinating experiment, with the design of, the protection of from outside forces, and the measurement of results ingenious. Thank you for the reference.