The Copernican

An enigma by any name

At the centre of the Milky Way galaxy, there is thought to be a supermassive black hole christened Sagittarius A*.   | Photo Credit: Picasa

Isaac Newton imagined the gravitational force to be the never-repulsive force that acted on all massive bodies. And in imagining so, the biggest problems of his time were presented by the motion of planets in the Solar System around the Sun. In 1684, >Christopher Wren, Robert Hooke and Edmund Halley met at a coffee shop in England to discuss planetary physics. In their conversation, the doubt arose as to what the shape of the path was that a planet took in its journey around the Sun.

Following this meeting, Halley paid a visit to Newton in an attempt to get the question answered. When asked, Newton didn't hesitate to say they'd be elliptical. When asked for the solution, Newton told Halley that he'd misplaced it and would recreate it for him soon. This incident is acknowledged to have prompted Newton to compose his Philosophiae Naturalis Principia Mathematica in the next 18 months. And in the Principia, Newton had this paragraph:

" From the three last Propositions it follows, that if any body P goes from the place P with any velocity in the direction of any right line PR, and at the same time is urged by the action of a centripetal force that is inversely proportional to the square of the distance of the places from the centre, the body will move in one of the conic sections, having its focus in the centre of force; and conversely."

While Newton says the path is conical—like an ellipse—he doesn't provide a proof, and so Halley's request went unanswered. Nevertheless, the Principia became the first major work of science in centuries and provided the dominant foundation for at least two more centuries of physical study.

In 1783, the geologist John Michell >wrote a letter to the chemist Henry Canevdish discussing the masses and motion of celestial bodies in which he contemplates the idea of a star so dense that even light cannot escape it. This idea was discouraged because it >disagreed with the Newtonian zeitgeist of the time. In fact, there were so many things dreamt of in his philosophy that it was not until Albert Einstein's coming that the theory of gravitation could accommodate all the paradigm-altering discoveries that had been made until then.

The continuum

And in his turn, Einstein birthed >the beginnings of an outrageous legacy in 1915, when he published his first paper on general relativity. This theory presented a new way of looking at gravity: it was no longer just the force that acted on all massive bodies but also the force that arose out of the curvature of the space-time continuum.

The theory of general relativity (GR) works out well on paper. To date, a few experimental proofs of the theory have been acquired ( >gravitational lensing, for one). However, the outrageousness stems from a unique possibility—even >a Gödelian inconsistency—that GR allows for: the black hole.

To employ the cliché, imagine space-time to be a fabric of smooth weave that you’re holding between your outstretched arms. Now, imagine how the weave would bend down if you dropped a heavy marble onto it. That’s how space-time would be bent, too, if the marble were Earth. And the bending would be attributed to Earth’s gravitational field.

In another instance, instead of a marble, drop a bowling ball onto the fabric. Assuming you’re unable to carry the weight, you let the ball and the fabric drop to the floor, where it is completely wrapped around the ball.

This is what happens to space-time in the presence of a black hole. There is a distortion of the continuum—as if the ‘rest’ of space-time cannot reach within the black hole itself. Even though its tremendous gravitational strength is understood to be centred at its core, a black hole is thought to begin to the world outside at the event horizon, the distance from the black hole beyond which it is impossible to escape its pull.

They are formed when the gravitational field in a volume of space collapses inward to some point. Such a collapse is thought to be triggered when a suitably heavy star runs out of fuel, blows away its outermost gaseous layers, while the rest of the star is unable to resist the gravitational temptation of shooting into the core.

>If the star is heavier than the Chandrasekhar limit but lighter than the >Tolman-Oppenheimer-Volkoff (TOV) limit, the inward collapse is prevented by the formation of a smaller neutron star, at which point there is a bounce-back followed by a vicious titanic explosion called a supernova. If the star is heavier than the TOV limit, then the inward collapse could result in the formation of a black hole— >one of the better understood processes of black-hole formation.


Thanks to the ‘Golden Age of general relativity’ in the mid-20th century, we’re in a position to better understand these enigmatic objects. Some of the notable physicists who made heady theoretical progress in this era include David Finkelstein, Werner Israel, Ezra Newman, James Bardeen, Roy Kerr, Evgeny Lifshitz, Brandon Carter, Jacob Bekenstein, Roger Penrose and Stephen Hawking.

Among them, Stephen Hawking is to this day considered to be the first-among-equals when it comes to expertise on black holes. Alongside Bardeen, Bekenstein, Carter, Penrose and others, Hawking was responsible for establishing many properties of black holes and how they could be determined. Around this time, an interesting paradox was discovered by Hawking and Bekenstein about black holes—the beginnings of a problem that Hawking attempted to resolve last week.

In 1974, they discovered—theoretically—that black holes emit some radiation, as if it was running a fever on account of all that it had swallowed. This radiation is called Hawking radiation. The heavier a black hole is, the weaker is its Hawking radiation.

Conversely, smaller black holes should be letting off their energy faster through Hawking radiation and, hypothetically, completely evaporate over time. In fact, NASA’s >Fermi telescope is out there orbiting Earth while looking out for this black-hole wheeze in the darker depths of space.

“Black holes have no hair”

In the meantime, in 1973, the physicists Charles Misner, >Kip Thorne and John Wheeler had established the intriguingly titled >no-hair theorem. They argued that no matter the process of formation of a black hole, all black holes could be understood in terms of three basic properties: mass, electric charge, and angular momentum.

So, no matter if a black hole had formed by the inward collapse of a bucket, a heavy star or the Solar System, it will be describable only in terms of its mass, electric charge, and angular momentum.

Now, imagine a black hole has already formed and you lob a bucket, a screwdriver and a building into it. Despite the initial nature of these objects, the black hole would emit Hawking radiation that is compositionally identical—in its randomness—in all three cases. And thanks to the no-hair theorem, the black hole’s characteristics also wouldn’t change.

For physicists, >this is unacceptable because where, then, is the information of the bucket, the screwdriver, the building? Is it lost?

The dying astronaut

There are many competing answers to this problem: the information paradox. Between some ten options presented over the years, they violate one of, or a combination of, the law of conservation of energy, existing theories of gravity, the laws of black-hole thermodynamics, the viewpoint that nature evolves with time, quantum theory, and GR.

One among these options was proposed by American physicist Joseph Polchinski; it is notable because it was an extension to this option that Hawking submitted a paper on January 22, drawing the attention of the world’s media. In 2012, Polchinski and two of his students at the Kavli Institute for Theoretical Physics, California, were wondering what would happen to an astronaut should he fall inside a black hole. Specifically, they were wondering how he would die.

As he started to sink toward the black hole’s centre, the gravitational force on him would continuously build up. Over time, he’d realize the part of his body closer to the centre was being pulled on stronger than the part farther away. Soon, because of this difference, he’d be ripped apart before all his parts would be compressed and, well, digested.

… but there was an issue.

Their calculations showed that quantum mechanical effects on the black hole’s event horizon would almost instantaneously burn the astronaut “to a crisp”, an outcome that contradicted general relativity. At the same time, the firewall idea was useful because it appeared to resolve the information paradox. According to Polchinski, the information of doomed objects would be stored in terms of its impact on all energy radiated from the black hole.

However, the violation of GR still remained. So, when Polchinski attempted to craft a scenario in which such a firewall doesn’t form, he was startled: he couldn’t do it without violating quantum mechanics.

Here was another paradox.

As physicist Raphael Bousso >told Nature, the firewall idea “essentially pits quantum mechanics against general relativity, without giving us any clues as to which direction to go next.” Seen another way, it seems a solution would be found only in the conciliation of quantum theory and GR, a feat proving unachievable to this day.

Hawking’s solution(s)

At the 17th International Conference on General Relativity and Gravitation in Dublin, 2004, Hawking suggested that the information was never lost. His solution required that a ‘true’ event horizon never formed around a black hole, simply an ‘apparent horizon’ that let information gradually leak out.

At the time, this apparent solution meant Hawking losing a bet against another physicist, John Preskill, who had said that, of course, information wouldn’t be lost inside a black hole. On the other hand, the other person who had sided with Hawking against Preskill, >Kip Thorne, couldn’t agree with Hawking’s solution.

And now, 10 years later, Hawking has expanded on the idea of this ‘apparent horizon’. In a yet-to-be-published paper titled ‘Information Preservation and Weather Forecasting for Black Holes’, Hawking has postulated that information that has gone inside a black hole isn’t lost, but actually comes out in a wildly mangled form.

Moreover, he has argued that although the information is there in that form, attempting to reconstruct it into what it was would be almost impossible—like forecasting weather. Essentially, he's trying to eke out a solution that minimally violates quantum theory and GR. Even though this would change the mathematics behind physicists’ calculations, astronomers wouldn’t see any difference—if they were looking at a black hole, they’d still be looking at what seems like the event horizon even if it is, in fact, the apparent horizon.

So, through the years, our understanding of gravity has evolved—first on the basis of what we could observe, then to what we could speculate based on what we thought we knew, and then on to conceiving solutions based on what we think could be—to have become more discrete. Simultaneously, it seems only eventual that as we resolved the mechanisms of the cosmos by the principles of GR, the dominant theory of physics outside a black hole, and the effects of a singularity by the principles of quantum theory, our ultimate solution seems to lie at the boundary between the two: the event horizon.

And if Hawking is to be believed, event horizons would no longer even be the defining property of black holes.

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Printable version | Nov 24, 2020 1:24:44 AM |

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