Robert McNees
Happy Rotating Black Hole Day!
Roy Kerr submitted his breakthrough paper describing the spacetime around a rotating black hole #OTD in 1963.
Physicists had been searching for decades for this solution to the field equations of Einstein's theory of general relativity.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.11.237
Robert McNees
Subrahmanyan Chandrasekhar, who established that stars of a certain mass would inevitably collapse into black holes, described his reaction to Kerr's solution as "shuddering before the beautiful."
He wrote:
Robert McNees
Kerr's paper appeared in print on September 1st of that year, so I guess you could just as well call that "Rotating Black Hole Day.”
But why pass up an (admittedly gimmicky) opportunity to talk about black holes?
Kerr, who is from New Zealand, was spending a year at UT-Austin when he wrote and published his breakthrough paper. He was one of the first visiting scientists at Alfred Schild's new Center for Relativity.
Robert McNees
He announced his result at the 1st Texas Symposium on Relativistic Astrophysics (these mostly biennial meetings still take place). The meeting was convened to discuss quasars, which had only recently been discovered.
As the story goes, Kerr's esoteric topic prompted many in the audience to leave or ignore the talk!
Achilles Papapetrou, a giant of the field, was furious. He stood and demanded the crowd's attention, noting that he himself had tried and failed to solve the problem for 30 years.
Robert McNees
Relativists quickly realized the importance of what Kerr had done.
Subrahmanyan Chandrasekhar said that realizing the Universe was full of "untold numbers" of black holes described by Kerr's solution was "the most shattering experience" of his scientific career.
http://www.parrikar.org/essays/shakespeare-newton-beethoven-page3/
Robert McNees
Kerr was already visiting the US Air Force's Aerospace Research Laboratories in Ohio before he arrived at UT.
It makes sense that UT had a relativity center. The field had been revived by Wheeler et al in the 1950s, and UT was flush with oil money. It was easy for Schild to convince them to support his research center.
But why was the Air Force hosting relativists? Bergmann and Goldberg had convinced them that relativity was essential to national defense, and there's always Defense money.
Robert McNees
Before saying any more about Kerr's solution, there's a very sad story attached to this worl.
The Kerr metric is usually presented in "Boyer-Lindquist" coordinates, which makes its nature as a rotating, axisymmetric, spherical object more apparent.
They submitted their paper presenting these coordinates in July of 1966.
Robert McNees
Both Boyer and Lindquist were visiting the UT Center for Relativity at the time.
Just a few weeks later, on August 1, Boyer was walking across campus when he became the third victim of mass murderer Charles Whitman, the UT Clock Tower shooter.
Lindquist had to add the following note to their paper.
Robert McNees
There are many interesting things to say about Kerr's rotating black hole solution of Einstein's equations. Let me highlight just a few.
First, the structure of spacetime around a rotating black hole is qualitatively more complex than the Schwarzschild black hole, which does not rotate.
Indeed, 47 years passed between the discovery of Schwarzschild’s and Kerr’s solutions.
Robert McNees
Like the Schwarzschild black hole, Kerr's solution has an event horizon demarcating a region of spacetime which a person, dog, or spaceship can enter but not leave.
(In fact, it has two — an inner horizon and an outer horizon. For our purposes only the outer horizon is relevant.)
The (outer) horizon for a Kerr black hole is smaller than that of a Schwarzschild black hole with the same mass. If it is spinning very slowly, they are about the same.
Robert McNees
As it spins faster, the horizon gets smaller. There is an upper limit on how rapidly the black hole can spin. When it reaches this "extremal" limit, its horizon is just half the Schwarzschild radius.
But the really interesting stuff is happening outside the horIzon, where the black hole’s rotation drags space time along with it.
There is a region called the “Ergosphere” where this dragging is so powerful that it is not possible to remain at rest!
Robert McNees
Here is a “cross section” of a Kerr black hole.
The ergosphere is the light blue region outside the horizon. One can move in and out of the ergosphere, but it is not possible to remain at rest once inside. One *must* move in the direction of the black hole’s rotation.
(Note: When thinking about black holes, it is often a good idea to view relativity as describing rules for how and where things are allowed to move, rather than sticking with Newtonian ideas like forces and accelerations.)
Robert McNees
The structure of spacetime around a Kerr black hole leads to lovely and complex orbits.
Check out @duetosymmetry’s app that lets you visualize the orbits of a photon outside a rotating black hole:
Robert McNees
In the late 60s/early 70s, Roger Penrose suggested a mechanism by which energy might be extracted from Kerr’s marvelous rotating black hole.
This is now refered to as the "Penrose Process." It works as follows.
You and a friend venture into the ergosphere. When they aren't looking, you push them towards the horizon. If you arrange things just right, conservation of energy and momentum results in you exiting the ergosphere with more energy than the two of you had going in.
Robert McNees
I am sorry you had to do this your friend, but science requires sacrifice and also the ravenous rotating maw of the dark lord of spacetime demands tribute.
Robert McNees
Anyway, the energy you acquire had to come from somewhere. It came from the black hole, which loses mass and angular momentum via this process.
It does so in a way that prevents the area of the horizon from decreasing, respecting Hawking’s black hole area law.
You can keep doing this for a while, but you get less out of it as the black hole loses mass and angular momentum. Eventually, it spins down and you have a Schwarzschild black hole with less mass than the original rotating black hole.
Robert McNees
The best case scenario starts with an "extremal" black hole — one that is spinning as rapidly as possible. In that case one could, in principle, convert something like 29% of the black hole's original mass into energy.
That’s an awful lot of energy.
Happy rotating black hole day!
Slothdude
@mcnees Also, presumably, you will be low on friends by then.
Robert McNees
@slothdude friend-limited process
Debbie Goldsmith 🏳️⚧️🏳️🌈
@mcnees I, for one, welcome our singular overlords.
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