I found this document to be extremely helpful in explaining space-time frame-dragging & other spinning black hole phenomena: http://www.eftaylor.com/pub/SpinNEW.pdf In Newtonian space, the Earth can revolve about the Sun at any inclination to the Sun's equator without "feeling" the Sun's own rotation. In GR, this isn't possible, as the Sun's rotation "drags the space-time frame" about itself. Consider "dropping" a test mass from infinity (_zero angular momentum_ about the Sun) into the Sun. In Newtonian space, the test mass would go all the way to the center of the Sun. In GR, this test mass would be deflected slightly from the center of the Sun by the "frame-dragging" of the Sun's rotation. Here's the cool part: the test mass would _still have zero angular momentum_ in the dragged space-time frame ! Thus, a test mass dropped towards a spinning black hole would end up rotating about the black hole center, but this rotation would be that of the space-time frame itself, as the test mass would still have zero angular momentum! At 09:42 AM 10/23/2014, Fred Lunnon wrote:
See http://en.wikipedia.org/wiki/Ergosphere << The equatorial (maximum) radius of an ergosphere corresponds to the Schwarzschild radius of a non-rotating black hole; the polar (minimum) radius can be as little as half the Schwarzschild radius if the black hole is rotating maximally. >>
This article later observes gnomically << Within the ergosphere, spacetime is dragged along in the direction of the rotation of the black hole at a speed greater than the local speed of light in relation to the rest of the universe. >> I sort of understand what this is getting at; but what precisely does it mean?
WFL
On 10/23/14, Henry Baker <hbaker1@pipeline.com> wrote:
I recently attended a lecture by a Caltech professor on the subject of Black Holes.
With a large % of non-technical people in the audience, she was trying to avoid getting extremely technical, but may have confused people even more.
One question was "what is the size of a black hole of 2 million solar masses?"
I found a web site that performs this exact calculation for _non-spinning_ black holes, and the answer seems to be that the radius of the event horizon is ~0.08 AU -- i.e., 8% of the distance from the Sun to the Earth.
The next question is what is the size of the fastest _spinning_ black hole with a mass of 2 million solar masses?
I wasn't able to find a calculator for this, but I did find a ppt slide that seemed to indicate that an extreme Kerr black hole had 1/2 the Schwarzchild radius of a non-spinning black hole; i.e., 0.04AU for my 2 million solar mass example. Apparently, this counterintuitive result comes from the fact that a large proportion of the spinning black hole mass is in the form of rotational energy.
Now a spinning black hole has an ellipsoidal "ergosphere" that touches the Schwarzchild radius at its poles, but is larger (?) at the equator (?)
What exactly is the shape of this ellipsoid for the fastest spinning black hole? To be precise, what is the numerical value of the eccentricity of the ellipse?
The "singularity" for a spinning black hole is no longer a point, but a _ring_. What formula gives me the _radius_ of this ring for a maximally spinning Kerr black hole ?