spinning black holes--2/18/2026

18 Feb 2026

spinning black holes--2/18/2026

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Today's selection-- from The Biggest Ideas in the Universe by Sean Carroll. Spinning black holes:

“The Earth is approximately spherical, but not quite: It is just a bit oblate, with the distance between the poles being shorter than the diameter along the equator by about 0.3 percent. Moreover, the Earth is lumpy, with deep oceans and tall mountains. As a result, the Earth's gravitational field is not quite uniform, and orbiting satellites have provided precise maps of exactly where the Earth's gravity is a bit stronger or weaker than average. Other planets will generally have their own features of local interest; the gravitational field of a planet can be highly distinctive.

“Not so for black holes. They are not lumpy. On the contrary, there is an idea called the no-hair theorem (although mathematicians call it the ‘no-hair conjecture,’ since it hasn’t been rigorously proven). Every black hole settles down to a state that is entirely characterized by its mass, electrical charge, and spin. Any two black holes with the same values of those quantities will have the same gravitational fields. That’s going to hold no matter what went into making them. A black hole created by the collapse of a massive star will end up looking exactly the same as one made from an equivalent amount of library books of peanut butter. The latter cases probably don’t occur in nature, but if they did, you couldn’t tell by examining the resulting black hole.

“Black holes with electric charge but no spin will have a spherically symmetric electric field around them, much like a charged particle would. That electric field contains energy, which has to be accounted for when solving Einstein's equation. The metric for such a black hole is given by the Reissner-Nordstrom solution, which was derived soon after the Schwarzschild solution by a number of people. That'snot so surprising; since everything is still spherically symmetric, the solution isn't all that different from Schwarzschild.

“At least on the outside. The Reissner-Nordström solution, taken at face value and pushed as far as it can go, describes an infinite series of black holes connecting separate universes, all hidden behind the event horizon.

Rotating black hole from the perspective of the distant observer. The different frames show the black hole from different angles.

“This is why you shouldn't always find exact solutions to equations and take them at face value, especially when extended beyond the physical situation they were intended to describe. Even the Schwarzschild solution, when maximally extended, describes two different universes connected by a wormhole. This fact was realized by Ludwig Flamm in 1916 and rediscovered by Einstein and his collaborator Nathan Rosen in 1935, so the Schwarzschild wormhole is sometimes called an Einstein-Rosen bridge. But nobody believes that real black holes out there in our galaxy are hiding wormholes and extra universes behind their event horizons. That's because real black holes aren't precisely empty space (or electric field) everywhere. They are formed by infalling matter, and the existence of that matter affects the spacetime metric in important ways. As a result, real black holes have singularities inside, but not gateways to other universes.

“It took a lot longer to find the metric for a spinning black hole, which was eventually derived by Roy Kerr in 1963 and is now called the Kerr solution. The difficulty stems from the lack of spherical symmetry; there is a preferred direction, the axis of rotation of the black hole. But Kerr's work was much more than a mathematical tour de force. In the real world we don't expect black holes to have substantial electric charge; if one did, it would quickly be neutralized by attracting and absorbing particles of the opposite charge. But we do expect black holes to be rotating, and rapidly so. Almost every black hole in the universe will be accurately described by the Kerr metric.”