On November 7th, Henry should get an excellent visual answer to his question about the shape of the ellipsoid for the fastest spinning black hole. I learned today about the upcoming November 7th release of the movie Interstellar. The story of the movie's development is that Carl Sagan set Kip Thorne up with a blind date with Lynda Obst, a moviemaker, three decades ago. Kip and Lynda recently began toying with ideas for a movie involving mysterious properties of black holes and wormholes. Spielberg, and the Nolan brothers, Jonathan, a screenwriter, and Chris, who directed Memento, Inception, and Batman, began developing the movie. Chris began meeting with Thorne to get a handle on the science. Thorne says that "great science" was embedded in the movie from the beginning. Thorne said that, for time dilation, they'd need a supermassive black hole spinning close to the speed of light. Special effects guy Paul Franklin asked Thorne to specify the math that was needed. Thorne wrote heavily-researched and sourced memos specifying the necessary equations. 30 programmers took a year and thousands of computers to develop the new renderer. Single frames took up to 100 hours to render. The team thought that artifacts in the rendering indicated bugs in the program. Thorne took a look and realized the program's implementation was correct and had uncovered something inherent in the math but completely unexpected. The warped space around the black hole warps the accretion disk. Light trapped around the disk has a complex fingerprint near the shadow. The disk appears above the black hole, below it, and in front of it. Thorne says he'll get at least two papers out of the results. The images are said to be beautiful, and, of course, that would be true in many different ways. This is the first time I can remember being quite excited about an upcoming movie release. http://www.wired.com/2014/10/astrophysics-interstellar-black-hole/ Jeff On Thu, Oct 23, 2014 at 12:21 PM, 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 ?

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun