### Spinning Black Holes Are a Drag

When you release a lot of black hole results to the public, you can sometimes forget how weird these objects are. We focus on the significance and the novelty of the result, rather than the exotic features that are common to many black holes. A recent paper reminded me about the latter and highlighted one of the curiosities of General Relativity, concerning the distortion of spacetime near these extreme objects. This post discusses some of the physics of spinning black holes.

In late February, NASA released a new result where the authors "measure definitively, for the first time, the spin rate of a black hole with a mass 2 million times that of our sun." In their press release, written by Whitney Clavin and her JPL colleagues, they say that the supermassive black hole is "spinning almost as fast as Einstein's theory of gravity will allow". These are results from NASA's Nuclear Spectroscopic Telescope Array (NuSTAR), the new X-ray kid on the space block, and the European Space Agency's XMM-Newton. The 1st author of the paper is Guido Risaliti from the Harvard-Smithsonian Center for Astrophysics (my home institution) in Cambridge, Mass., and the Italian National Institute for Astrophysics. The supermassive black hole is located in the middle of a beautiful galaxy called NGC 1365.

Guided by the press release, a NASA press conference, the science paper and a News and View article in Nature, science writers tackled the story. There are details about how the data enabled the authors to reach their conclusions, but I will focus on the basic result, the rapid spin of the black hole and how it was described. I'll also give some thoughts on how it

The Bad Astronomer, Phil Plait, wrote at his Slate blog about the author's observations of the black hole and how they "were surprised to find out it's spinning so fast that the outer edge is moving at very nearly the speed of light!"

An LA Times article by Amina Khan has a headline of "X-rays show galactic black hole spinning near speed of light" and says the black hole "is spinning at 84% of the maximum possible rate" following the paper and the News and Views article. It also says:

I looked back at how

For Cygnus X-1 we said:

For the sample of nine black holes we include a quote from astrophysicist Rodrigo Nemmen:

Other explanations are useful, but they're not as clear. For example, the one by Risaliti gives a good explanation of the energy a spinning supermassive black hole has, but this is more useful for stories explaining the black hole's effect on their host galaxy. It also doesn't explain how fast the spin is or what is spinning. The answer by Harrison explains how fast the event horizon is spinning but it does not mention that an infinitely powerful rocket would be required to stand still near the event horizon of a spinning black hole, both to prevent infall and rapid spin.

There is a subtlety regarding the 84% number quoted above. This refers to the quantity a* used by astronomers that is a measure of the angular momentum of the black hole, which itself depends on its mass and speed. This quantity a* is defined so that its maximum value is 1.0 for a black hole with an event horizon rotating at the fastest speed allowed, the speed of light. For no spin a*=0. For the black hole in NGC 1365, a* was estimated to be at least 0.84. However, this does

speed = (a*/(1+sqrt(1-a*^2))) c

provided by Robert Penna, where "c" is the speed of light. So, when a*=0.84 the speed is 0.54c, or just over half the speed of light.

This point is more pedantic than interesting, but it helps set up a related issue. Let's return to the stellar-mass black hole Cygnus X-1. The rate of spin given above for this black hole comes from a spin frequency estimate. The spin frequency of a black hole measured at the event horizon depends only on a* and the black hole's mass. For Cygnus X-1, if a*=1 then the spin frequency is 1091 Hz, that is spacetime at the event horizon would spin around 1091 times a second. That's mind-bogglingly fast, but it isn't the interesting numerical point that I want to make.

What happens when you double-check that the speed of the event horizon - in this extreme case of a*=1 - is the speed of light? The radius of the event horizon for Cygnux X-1 is 21.9 km. So, the speed of the horizon should be the circumference of the event horizon multiplied by the spin frequency, ie 2*pi*21.9*1091 km/s. But this only equals ~150,000 km/s, which is half the speed of light. What's going on here?

The answer is that our assumption about the geometry was wrong. Near a black hole the normal geometry that we learned in school doesn't apply and the circumference of a circle is

For some explanations and more details about how geometry is distorted near a black hole, you can check the illustrations and descriptions in "Black Holes and Time Warps: Einstein's Outrageous Legacy" by Kip Thorne given here and in "The Physical Universe: An Introduction to Astronomy" by Frank Shu given here.

I asked Penna what happens to the velocity of spacetime

In late February, NASA released a new result where the authors "measure definitively, for the first time, the spin rate of a black hole with a mass 2 million times that of our sun." In their press release, written by Whitney Clavin and her JPL colleagues, they say that the supermassive black hole is "spinning almost as fast as Einstein's theory of gravity will allow". These are results from NASA's Nuclear Spectroscopic Telescope Array (NuSTAR), the new X-ray kid on the space block, and the European Space Agency's XMM-Newton. The 1st author of the paper is Guido Risaliti from the Harvard-Smithsonian Center for Astrophysics (my home institution) in Cambridge, Mass., and the Italian National Institute for Astrophysics. The supermassive black hole is located in the middle of a beautiful galaxy called NGC 1365.

*should*be described, given the luxury of time.
This artist's concept illustrates a supermassive black hole with millions to billions times the mass of our sun. Supermassive black holes are enormously dense objects buried at the hearts of galaxies. (Smaller black holes also exist throughout galaxies.) In this illustration, the supermassive black hole at the center is surrounded by matter flowing onto the black hole in what is termed an accretion disk. This disk forms as the dust and gas in the galaxy falls onto the hole, attracted by its gravity. Also shown is an outflowing jet of energetic particles, believed to be powered by the black hole's spin. The regions near black holes contain compact sources of high energy X-ray radiation thought, in some scenarios, to originate from the base of these jets. This high energy X-radiation lights up the disk, which reflects it, making the disk a source of X-rays. The reflected light enables astronomers to see how fast matter is swirling in the inner region of the disk, and ultimately to measure the black hole's spin rate. [
Caption reproduced from this NASA site] Credit: NASA/JPL-Caltech |

The Bad Astronomer, Phil Plait, wrote at his Slate blog about the author's observations of the black hole and how they "were surprised to find out it's spinning so fast that the outer edge is moving at very nearly the speed of light!"

An LA Times article by Amina Khan has a headline of "X-rays show galactic black hole spinning near speed of light" and says the black hole "is spinning at 84% of the maximum possible rate" following the paper and the News and Views article. It also says:

"If you were standing near the event horizon of this particular black hole, you would have to turn around because your space-time is twisting," NuSTAR lead scientist Fiona Harrison, a Caltech astrophysicist, said at a news conference. "You would be turning around once every four minutes just to stand still."An article in Physics World by Hamish Johnston says:

"The study confirms that the SMBH is spinning at a rate close to the limit defined by the general theory of relativity. While the rotational properties of a spinning gravitational singularity are difficult to describe in a simple way, Risaliti explains that the rotational energy of the SMBH at the heart of NGC1365 is about the same as the energy that is given off by a billion stars burning for a billion years."That's three different stories giving different ways to describe the spin. I think Johnston explains the challenge well. How do you describe the properties of a spinning singularity in a simple way? To answer this question well I think it's useful to explain what is doing the spinning. Plait discusses the "very edge of the black hole" and he's presumably talking about the event horizon, the region surrounding the black hole that light cannot escape beyond. The event horizon is an important boundary, but it isn't a physical object, like a wall (unless some recent speculation about black hole firewalls is correct, as explained in this article by Jennifer Ouellette). If material makes it to the event horizon, as must occur regularly for some supermassive black holes, including the one in NGC 1365, it won't last there for long.

I looked back at how

*we*have previously described black hole spin with Chandra results. We did a press release for Cygnus X-1, a black hole in our galaxy that is about 15 times as massive as the Sun, and a different press release for a group of nine supermassive black holes.For Cygnus X-1 we said:

"the black hole is spinning at very close to its maximum rate. Its event horizon -- the point of no return for material falling towards a black hole -- is spinning around more than 800 times a second."That's a very impressive number and it's accurate, but it doesn't explain what is spinning.

On the left, an optical image from the Digitized Sky Survey shows Cygnus X-1, outlined in a red box. Cygnus X-1 is located near large active regions of star formation in the Milky Way, as seen in this image that spans some 700 light years across. An artist's illustration on the right depicts what astronomers think is happening within the Cygnus X-1 system. Cygnus X-1 is a so-called stellar-mass black hole, a class of black holes that comes from the collapse of a massive star. The black hole pulls material from a massive, blue companion star toward it. This material forms a disk (shown in red and orange) that rotates around the black hole before falling into it or being redirected away from the black hole in the form of powerful jets. [Caption reproduced from this Chandra website] Credit: Optical: DSS; Illustration: NASA/CXC/M.Weiss |

"We think these monster black holes are spinning close to the limit set by Einstein's theory of relativity, which means that they can drag material around them at close to the speed of light".That's very close to the best answer. It's

*spacetime itself*that is rotating at almost the speed of light in one of these black holes, and this is what drags material around with it at the same speed. (The technical term for this is "frame-dragging", as Matthew Francis explains in his Ars Technica article in more detail.) I checked with Robert Penna, a local expert on General Relativity and black holes, who confirmed this explanation. Here's the description he gave:"A good mental picture is to think of the spacetime around a spinning black hole as a whirlpool. Objects are dragged around by spacetime as they fall towards the hole. At the horizon they are forced to rotate at the angular velocity of the whirlpool."

A subset of a sample of nine large galaxies is seen on the left of this graphic. These Chandra images show pairs of bubbles created in the gaseous atmospheres of the galaxies that were created by jets produced by giant central black holes. These data were used to help determine that the supermassive black holes are likely to be spinning very rapidly. The artist’s illustration (right) depicts how material very near the black hole falls inward and joins a rapidly spinning disk of matter. Most of this material is swallowed by the black hole, but some of it is swept outward in jets (colored blue) by quickly spinning magnetic fields close to the black hole. [Caption reproduced from this Chandra website] Credit: NASA/CXC/UFRGS/R.Nemmen et al.; Illustration: NASA/CXC/M.Weiss |

There is a subtlety regarding the 84% number quoted above. This refers to the quantity a* used by astronomers that is a measure of the angular momentum of the black hole, which itself depends on its mass and speed. This quantity a* is defined so that its maximum value is 1.0 for a black hole with an event horizon rotating at the fastest speed allowed, the speed of light. For no spin a*=0. For the black hole in NGC 1365, a* was estimated to be at least 0.84. However, this does

*not*mean that the black hole's*speed*is at least 84% of the speed of light. The speed is given by this formula:speed = (a*/(1+sqrt(1-a*^2))) c

provided by Robert Penna, where "c" is the speed of light. So, when a*=0.84 the speed is 0.54c, or just over half the speed of light.

This point is more pedantic than interesting, but it helps set up a related issue. Let's return to the stellar-mass black hole Cygnus X-1. The rate of spin given above for this black hole comes from a spin frequency estimate. The spin frequency of a black hole measured at the event horizon depends only on a* and the black hole's mass. For Cygnus X-1, if a*=1 then the spin frequency is 1091 Hz, that is spacetime at the event horizon would spin around 1091 times a second. That's mind-bogglingly fast, but it isn't the interesting numerical point that I want to make.

What happens when you double-check that the speed of the event horizon - in this extreme case of a*=1 - is the speed of light? The radius of the event horizon for Cygnux X-1 is 21.9 km. So, the speed of the horizon should be the circumference of the event horizon multiplied by the spin frequency, ie 2*pi*21.9*1091 km/s. But this only equals ~150,000 km/s, which is half the speed of light. What's going on here?

The answer is that our assumption about the geometry was wrong. Near a black hole the normal geometry that we learned in school doesn't apply and the circumference of a circle is

*less*than 2*pi times the radius, because of the severe distortion of spacetime. When you use the correct geometry you find that that the speed of the event horizon for a black hole with a*=1 is the speed of light, as expected (I was assured that this is the case but I didn't do the calculation myself, since my General Relativity skills are a little rusty).For some explanations and more details about how geometry is distorted near a black hole, you can check the illustrations and descriptions in "Black Holes and Time Warps: Einstein's Outrageous Legacy" by Kip Thorne given here and in "The Physical Universe: An Introduction to Astronomy" by Frank Shu given here.

General Relativity and black hole expert Robert Penna. Credit: Robert Penna. |

*inside*the black hole's event horizon, but we don't even have a useful definition of velocity in this region. In Penna's words:"The velocity makes sense outside the horizon because there is a standard observer, the fixed observer at infinity [someone who is a very long distance away where the gravitational effects of the black hole are negligible]. This observer is not available inside the horizon, because an observer at infinity can't see across the horizon. And an observer inside the horizon can't be at rest: the severe gravity causes everything inside the horizon to fall towards the singularity. Different observers will measure different velocities, so there isn't a standard velocity inside the horizon."With black holes you have objects where normal geometry and physics do not apply and where material can be pulled along at almost the speed of light just before it disappears from the observable universe for ever. These points about geometry and physics are well established but can sometimes be neglected by astronomers and science communicators. Black holes should

*not*be taken for granted just because a lot of papers are published on them.**End-note:**I would like to thank Robert Penna for his thoughtful comments and also black hole expert Jeff McClintock, from Harvard Smithsonian Center for Astrophysics, who directed my questions to Robert.
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