Saturday, March 3, 2007

Black holes, anyone?

Empire of the Stars: Obsession, Friendship, and Betrayal in the Quest for Black Holes by Arthur I. Miller (2005)

This largely boringly written book – the best parts are the footnotes that discuss the findings dully presented in the text – chronicles the career of Subrahmanyan Chandrasekhar, who first proposed and calculated that there was an upper limit to the mass of a white dwarf: any white dwarf with a mass of over 1.4 times the solar mass would began a process of collapse that would lead to a singularity, a point of infinite density and zero volume. Chandra presented his findings in 1935, only to be met with harsh resistance, particularly from Arthur Stanley Eddington, then the pre-eminent astrophysicist in the world.

Miller tries to make a case that racism played a part in the professional response to Chandra’s calculation; certainly the professional goals of other prominent scientists led to the ignoring of Chandra’s findings, as did presuppositions from well-regarded scientists, like Eddington and Einstein, that the universe would not yield an infinite result. But to me, the story sounds all too typical of academia – the group in power wants results and conclusions that match up to their own way of thinking and are resistant to novelty. What else is new?

Although Chandra undoubtedly felt the condemnation from Eddington and the slighting of his work by his peers for the rest of his life (he was angry that he didn’t win the Nobel Prize twenty years earlier than he did), he went on to make significant findings in other fields away from astronomy, and did not seem to be professionally crippled by the experience, no matter how it wounded him personally.

Of greater interest in the book is the intellectual evolution towards the acceptance of black holes: from the 1935 negative reaction to the 1960s theorizing that indeed, black holes must exist, although evidence of their existence had not been found to date. There’s some cool stuff in this book about the nuclear arms race, hydrogen bombs, and the death of stars, but I really would never have finished this book if I hadn’t been stuck in an airport for 4 hours and wanted to avoid digging through my luggage for another book. It’s not the content, which could be fascinating. It’s the writing, dull as dishwater.

One fine example (pg 178): “Chandra had a keen eye for lurking stability problems; his forte was identifying the exact point at which a star is likely to collapse. He spotted a flaw in Gamow’s argument. The challenge was irresistible, and he decided to turn his attention to white dwarfs one last time.” Absorbing mystery yarn? Action-adventure for the teen-boy crowd? Cliched phrases, Alex, for $600!

Anytime reading the footnotes becomes more engrossing than the actual text, something is wrong. (One of the gems of the footnotes is that there may be white dwarfs that are diamonds, composed entirely of compressed carbon. Another is the story of Fuchs’ espionage.)

So unless anyone wants to know more from me about this book, I’ll put a black hole tutorial in this space.

(Abbreviated in parts from Stuart J. Robbins' site)

Classifications of black holes: mass, spin, and magnetic field

Stellar black holes: have a mass of 10-100 times the solar mass.

Supermassive black holes: have a mass of millions to even billions of solar masses.

Schwarzschild black holes: no spin and no magnetic field. It has two main components - a singularity and an event horizon. The singularity is what is left of the collapsed star, and is theoretically a point of 0 dimension with infinite density but finite mass. The event horizon is a region of space that is the "boundary" of the black hole. Within it, the escape velocity is faster than light, so it is past this point that nothing can escape.

Reissner-Nordstrøm Black Holes: no spin and a magnetic field. It has a singularity and two event horizons. The outer event horizon is a boundary where time and space flip. This means that the singularity is no longer a point in space, but one in time. The inner event horizon flips space-time back to normal.

Kerr Black Holes: spin and magnetic field. A Kerr black hole adds another feature to the anatomy - an ergosphere. The ergosphere resides in an ellipsoidal region outside the outer event horizon. The ergosphere represents the last stable orbit, and the outer boundary is called the static limit. Outside of it, a hypothetical spaceship could maneuver freely. Inside, space-time is warped in such a way that a spaceship would be drawn along by its rotation.

An interesting point that comes up in the case of a spinning black hole is that of the naked singularity. The faster the black hole rotates, the larger the inner event horizon becomes, while the outer event horizon remains the same size. They become the same size when the rotational energy equals the mass energy of the black hole. If the rotational energy were to become more than the mass energy, the event horizons would vanish and what would be left is a "naked singularity" - a black hole whose only part is the singularity.

Yet another distinguishing feature of the Kerr black hole is that, since it rotates, the 0-D point that is the singularity in the Schwarzschild and Reissner-Nordstrøm black hole is spun into a ring of 0 thickness. Interesting theoretical physics can take place around this ring singularity. One consequence is that nothing can actually fall into it unless it approaches along a trajectory along the ring's side. Any other angle and the ring actually produces an antigravity field that repels matter.

NOTE: The only physical part of a black hole is the singularity. The other parts mentioned are mathematical boundaries. There is no physical barrier called an event horizon, but it marks the boundaries between types of space under the influences of the singularity.

Two other features can characterize a black hole: accretion disk and jets.

An accretion disk is matter that is drawn to the black hole. In rotating black holes and/or ones with a magnetic field, the matter forms a disk due to the mechanical forces present. In a Schwarzschild black hole, the matter would be drawn in equally from all directions, and thus would form an omni-directional accretion cloud rather than disk.

The matter in accretion disks is gradually pulled into the black hole. As it gets closer, its speed increases, and it also gains energy. Accretion disks can be heated due to internal friction to temperatures as high as 3 billion K, and emit energetic radiation such as gamma rays. This radiation can be used to "weigh" the black hole. By using the doppler effect astronomers can determine how fast the material is revolving around the black hole, and thus can infer its mass.

Jets form in Kerr black holes that have an accretion disk. The matter is funneled into a disk-shaped torus by the hole's spin and magnetic fields, but in the very narrow regions over the black hole's poles, matter can be energized to extremely high temperatures and speeds, escaping the black hole in the form of high-speed jet.

Where do black holes come from?

Current theory holds that black holes form in three main ways. The first is that if a star has more than nine solar masses when it goes supernova, then it will collapse into a black hole. The reason that a neutron star stops collapsing is the strong nuclear force, the fundamental force that keeps the center of an atom from collapsing. However, once a star is this big, the gravitational force is so strong that it overwhelms the strong nuclear and collapses the atom completely. Now there is nothing to hold back collapse of the star, and it collapses into a point (or, in theory, a ring) of infinite density.

A second way for black holes to form is that, in some rare instances, two neutron stars will be locked in a binary relationship. Because of energy lost through gravitational radiation, they will slowly spiral in towards each other, and merge. When they merge, they will almost always form a black hole.

Finally, a third way was proposed by quantum cosmologist Stephen Hawking. He theorized that trillions of black holes were produced in the Big Bang, with some still existing today. This theory is not as widely accepted as the other two.

AG again, providing cool facts about black holes (see Hawking's Brief History of Time or Greene's The Elegant Universe for more):

Black holes aren’t really black. As proposed by Stephen Hawking, black holes emit a type of radiation due to escaping particles. The intense gravitational field near the event horizon of a black hole can briefly split a pair of photons apart. If one falls through the event horizon, the other particle, which would have been annihilated by its partner when they came into contact, is now left outside the black hole; indeed the energy from the fall of the one partner of the pair over the event horizon will give the other partner energy to move further away from the event horizon. The particles emitted from a black hole in this way are called Hawking radiation. Which leads to…

Black holes may evaporate. Although not yet observed, if blacks holes leak energy (through the Hawking radiation) we know from Einstein’s famous E = mc2 that the black hole will also lose mass. However, for a typical black hole, the evaporation time would amount to more than 1067 years (the age of the universe is around 109 years). But lightweight black holes formed in the first few moments of the Big Bang (according to Hawking’s calculations, less mass means higher temperature and hence more radiation) may exist and may be on the verge of evaporation, emitting Hawking radiation and gamma rays that could be picked up by observatories. Even more fascinating: as a black hole emits radiation, its mass shrinks and the distance between its center and the even horizon diminishes. As this happens, does the space that was previously in the black hole still contain its old information? Hawking has bet that black holes destroy the information.

Black holes have entropy. This was actually one of the starting problems that lead to the two solutions described above, formulated in 1974 by Hawking. Starting from these theoretical observations/calculations: the area of the event horizon increases in physical interactions (calculated by Hawking), and black holes must have entropy (Jacob Beckenstein), and with a whole lotta intuition and math, Hawking arrived at the above conclusions.

There may be massless black holes. Formed from a black hole that has lost its mass; these black holes would lack an event horizon. In string theory, the loss of mass is attributable to the shrinking of a piece of the Calabi-Yau portion of space to a point. (Calabi-Yau spaces are where the extra dimensions required by string theory can be curled up.)

And of course, this sci-fi question remains: at the singularity, where space-time is infinitely curved and time ends, could it be possible for another universe to be attached? String theory provides possible solutions, but that’s another discussion.

2 comments:

Aurelian said...

A fascinating and informative post, and as alluded to, actually more interesting in the tutorial section.

Of the review of "Empire of the Stars" the following quote seems to warn its narrative style is `boringly written' , which to an author like me, is a cautionary note to hear as something to avoid! The remark on making the footnotes interesting, on the other hand, is a good tip.

Anytime reading the footnotes becomes more engrossing than the actual text, something is wrong. (One of the gems of the footnotes is that there may be white dwarfs that are diamonds, composed entirely of compressed carbon. Another is the story of Fuchs’ espionage.)

So the real `gem' in this post turns out to be the `tutorial' on black holes. For its very obvious that alot of complex information from more than one source is nicely synthesized here. I didn't know that were three main types of black holes for examples, or that the presence or absence of a magnetic field and spin are how you classify them. To some extent, this derives from earlier readings about neutron stars, well recalled, but clearly out of date, lol, from the 80's. This post serves as a nice update.

Only a few points seemed unclear, and became uncertain of:

"Schwarzschild black holes: no spin and no magnetic field. It has two main components - a singularity and an event horizon. The singularity is what is left of the collapsed star, and is theoretically a point of 0 dimension with infinite density but finite mass. The event horizon is a region of space that is the "boundary" of the black hole. Within it, the escape velocity is faster than light, so it is past this point that nothing can escape."

Does the term heard `schwarzschild radius' then apply only to this one type of black hole? Or did he also coin or have named after him a more general description?

Second,

"There may be massless black holes. Formed from a black hole that has lost its mass; these black holes would lack an event horizon. In string theory, the loss of mass is attributable to the shrinking of a piece of the Calabi-Yau portion of space to a point. (Calabi-Yau spaces are where the extra dimensions required by string theory can be curled up.)
And of course, this sci-fi question remains: at the singularity, where space-time is infinitely curved and time ends, could it be possible for another universe to be attached? String theory provides possible solutions, but that's another discussion."


This was intriguing ------ Re-reading there, I got the impression the last paragraph applied to singularities in general, not the massless kind alone. Is that correct?

- Aurelian

AG said...

Oh, aurelian, you do know how I love sycophancy! Thank you for the questions.

Does the term heard `schwarzschild radius' then apply only to this one type of black hole? Or did he also coin or have named after him a more general description?

The Schwarzschild radius is the radius at which a certain mass would compress infinitely, with the result being a singularity. In other words, it's the radius at which the inward force of gravity overcomes the outward pressure of the mass. Thus, every mass has a Schwarzschild radius - a radius where if the mass were somehow crowded into those spatial dimensions, it would become a black hole. If all the mass of the sun were pushed into a radius smaller than a few miles, the sun would be a black hole - those couple of miles are the Sun's Schwarzschild radius. It is therefore also the event horizon of a non-rotating black hole. (Kerr black holes are a little more complicated because of the drag caused by angular momentum.)

The equation for it is actually wonderfully simple, requiring one to know only the mass of the object in question, as the gravitational constant (calculated from Newton's second law) and the speed of light are the other two factors.

For the average man weighing 75 kg, his Schwarzschild radius is 111 x 10^-27 m. For comparison, a QUARK is 10^-19 m. So imagine compressing your mass into something ten billion times smaller than a quark, if you wanted to become a black hole.

The Schwarzschild radius was actually known before Chandra's equations. Indeed, Chandra was inspired by Schwarzschild's work to arrive at his parameters for the size a white dwarf could be without becoming a black hole. However Schwarzschild, along with many others, thought stars should be modeled as incompressible fluids, with the outward degeneracy pressure always sufficient enough to counteract a collapse to infinity.

The impression the last paragraph applied to singularities in general, not the massless kind alone. Is that correct?

Yes, that last bit about singularities applies to all of these points of infinitely warped spacetime. A massless black hole, of course, would consist of only a singularity, but one can theorize as much as one wants about the features of that singularity and all singularities.