Black Holes: Seeking proof for the no-hair theorem

According to general relativity, a black hole has three measurable properties: mass, rotation (angular momentum), and electric charge.

That's it. If you know those three things, you know all there is to know about the black hole.

If the black hole is interacting with other objects, then the interactions can be much more complicated, but an isolated black hole is just mass, rotation (angular momentum) and electric charge.

In general relativity this is known as the no-hair theorem.

The basic idea of the no-hair theorem is that the material properties of any object (referred to as "hair" because a physicist named John Wheeler once coined the phrase "a black hole has no hair") become unmeasurable (hence unknowable) as the object collapses into a black hole.

On the surface this seems fairly reasonable. If a neutron star collapses into a black hole, for example, all the neutrons and their interactions become trapped inside the black hole's event horizon when the black hole forms.

The same would be true for an object that was lopsided (say with a mountain range on one side). As it collapses into a black hole, any irregularities would be squashed flat as it approaches the black hole limit.

But there are also difficulties with the no-hair theorem. For one, even though it's referred to as a theorem, it has never been proved in general relativity. So it really should be called the no-hair hypothesis.

There have been lots of demonstrations that the theorem is reasonable, and computer simulations tend to agree that black holes stabilise to a structure defined by mass, rotation (angular momentum) and electric charge, but none of these reach the level of proof.

Then there is the problem that if a black hole really is just defined by mass, rotation (angular momentum) and electric charge, then it has no temperature, and that means that its entropy is zero.

This violates the principles of thermodynamics. Of course when we try to include quantum theory into our black hole description we know that black holes do have a temperature.

In Stephen Hawking's theory, the temperature of a black hole depends upon its mass, so even a Hawking black hole would be definable by mass, rotation (angular momentum) and electric charge.

It's possible that the no-hair theorem is valid even for a quantum black hole.

But there is a more subtle mystery that hides within the no-hair theorem, because it would seem that a black hole is much simpler than other massive objects such as planets, stars and the like.

If you think about an object like the Sun, it has a certain chemical composition, and it's giving off light with different wavelengths having varying intensities.

There are sunspots, solar flares, convection flows that create granules, and the list goes on.

The Sun is a deeply complex object that we have yet to fully understand, and yet, if our Sun were compressed into a black hole, all that complexity would be reduced to mass, rotation (angular momentum) and electric charge.

So what happens when a complex object like a star collapses into a black hole? Where does all that complexity go?

In physics we refer to that complexity as the physical information of a system. According to quantum theory, physical information is never lost, but according to general relativity and the no-hair theorem, physical information that enters a black hole is lost forever.

This contradiction is known as the black hole information paradox, or sometimes the 'firewall paradox.'

Now you might think that the easy answer is just to presume the no-hair theorem is wrong but it's not that simple, and if we started exploring that paradox, things would get a bit hairy.

A 3-D model of stellar core collapse

A massive stellar core not quite managing to transition to a supernova explosion because of a small "kink" instability in its rotational axis. 

Credit: Philipp Mösta and Sherwood Richers

What happens when massive stars collapse? One potential result is a core-collapse supernova.

Astronomers can make observations of such events that tell us what is happening on the surface of a star when it explodes in a supernova, but it is considerably more difficult to know what is driving the process inside the star at its hot, dense core.

Philipp Mösta

Astrophysicists attempt to simulate these events based on the properties of different kinds of stars and knowledge of the fundamental interactions of mass and energy, hopefully providing astronomers with ready predictions that can be tested with observational data.

Christian Ott

In a recent publication, Caltech postdoctoral scholar Philipp Mösta and Christian Ott, professor of theoretical astrophysics, present a three-dimensional model of a rapidly rotating star with a strong magnetic field undergoing the process of collapse and explosion . . . or at least trying to.

Stars with a very rapid spin and a strong magnetic field are comparatively rare: no more than one in a hundred massive stars (those at least 10 times the mass of our sun) have these features.

According to Mösta and Ott's research, when these bodies undergo core collapse, small perturbations around its axis of rotation may inhibit the process that would ordinarily lead to a supernova explosion.

Previous models of the collapse of rapidly rotating magnetized stellar cores assumed perfect symmetry around the axis of rotation. In effect, these models were two-dimensional.

The models yielded the expectation that as these cores collapsed, the strong magnetic field combined with the rapid spin would squeeze the stellar material out into two narrow "jets" along the axis of symmetry, as shown at left.

Assuming perfect symmetry around the axis of rotation can be excused in part as a matter of simplifying the scenario so that it could be simulated on an ordinary computer rather than the kind of supercomputer that Mösta and Ott's three-dimensional simulations require: 20,000 processors to output 500 terabytes—over 500 trillion bytes—of data that represent only some 200 milliseconds in time.

But, says Ott, "Even working with paper and pencil, writing down equations and discussing them with other theoretical astrophysicists, we should have known that small perturbations can trigger an instability in the stellar core."

"Nothing in nature is perfect. As we learn from this model, even small asymmetries can have a dramatic effect on the process of stellar collapse and the subsequent supernova explosion."

More information: The paper, "Magnetorotational Core-collapse Supernovae in Three Dimensions," is available online: authors.library.caltech.edu/45202/1/2041-8205_785_2_L29.pdf

MIT Scientists develop new technique to measure mass of exoplanets

Artistic rendering of a planet's transmission spectrum. 

Credit: CHRISTINE DANILOFF /MIT, JULIEN DE WIT

To date, scientists have confirmed the existence of more than 900 exoplanets circulating outside our solar system.

To determine if any of these far-off worlds are habitable requires knowing an exoplanet's mass—which can help tell scientists whether the planet is made of gas or rock and other life-supporting materials.

But current techniques for estimating exoplanetary mass are limited. Radial velocity is the main method scientists use: tiny wobbles in a star's orbit as it is tugged around by the planet's gravitational force, from which scientists can derive the planet-to-star mass ratio.

Spitzer Space Telescope

For very large, Neptune-sized planets, or smaller Earth-sized planets orbiting very close to bright stars, radial velocity works relatively well.

But the technique is less successful with smaller planets that orbit much farther from their stars, as Earth does.

Now scientists at MIT have developed a new technique for determining the mass of exoplanets, using only their transit signal—dips in light as a planet passes in front of its star.

Julien de Wit

This data has traditionally been used to determine a planet's size and atmospheric properties, but the MIT team has found a way to interpret it such that it also reveals the planet's mass.

"With this method, we realized the planetary mass—a key parameter that, if missing, could have prevented us from assessing the habitability of the first potentially habitable Earth-sized planet in the next decade—will actually be accessible, together with its atmospheric properties," says Julien de Wit, a graduate student in MIT's Department of Earth, Atmospheric and Planetary Sciences.

De Wit is lead author on a paper published today in the journal Science, with co-author Sara Seager, the Class of 1941 Professor of Physics and Planetary Science.


Researchers at MIT explain what exactly an exoplanet or extrasolar planet is, why we study them and how you can detect them.

"The mass affects everything on a planetary level, such as any plate tectonics, its internal cooling and convection, how it generates magnetic fields, and whether gas escapes from its atmosphere," de Wit says.

"If you don't get it, there is a large part of the planet's properties that remains undetermined."

Using large telescopes such as the NASA's Spitzer and Hubble Space Telescopes, scientists have been able to analyze the transmission spectra of newly discovered exoplanets.

A transmission spectrum is generated as a planet passes in front of its star, letting some light through its atmosphere.

By analyzing the wavelengths of light that pass through, scientists can determine a planet's atmospheric properties, such as its temperature and the density of atmospheric molecules. From the total amount of light blocked, they can calculate a planet's size.

More information: "Constraining Exoplanet Mass from Transmission Spectroscopy," by J. de Wit et al. Science, 2013. DOI:10.1126/science.1245450

ESA Astronaut ISS Image: Weightless!

Mass but no weight. Moving experiment hardware.

Credit: ESA/NASA

NASA’s Solar Dynamics Observatory (SDO): Stereo Ahead coronal mass ejection

The STEREO (Ahead) spacecraft caught a large coronal mass ejection as it roared away from the Sun and out into space in the opposite direction from Earth (Feb. 26-28, 2011).

Inflatable Heat Shield Tested in Space

An inflatable heat shield was successfully tested on Monday, demonstrating for the first time that these light, flexible devices could be used to protect spacecraft on their way through planets' atmospheres.

Other spacecraft use solid heat shields that either drop away as the spacecraft near the surface, as happened with the Mars rovers, or gradually erode in the atmosphere.

These solid shields are heavy, and their weight limits the mass of the spacecraft they are designed to protect, since both must launch on the same rocket. Their physical size is also limiting, since the shields must be small enough to fit inside a launch rocket.

Balloon-like shields can in theory sidestep these issues, since they are lightweight and can inflate to relatively large sizes after being folded up during launch. These weight and size savings allow for heavier spacecraft payloads.

The new shield, called the Inflatable Re-entry Vehicle Experiment (IRVE), launched aboard a small rocket on Monday morning from NASA's Wallops Flight Facility on Wallops Island, Virginia. It was the first successful test of an inflatable heat shield.

"We're totally thrilled with the data results we've received," says project manager Mary-Beth Wusk of NASA's Langley Research Center in Hampton, Virginia.