Pedagoguery

Singularities in mathematics are points where a function is discontinuous or where it goes to infinity. For example, the function 1/x has a singularity where x = 0. When the equation represents some physical quantity, a singularity means that the laws of physics as we know it break down. This is what happens in general relativity at the heart of a black hole.

A black hole is actually made up of two parts: the singularity at the center, where density is infinite and the laws of general relativity break down, and the event horizon, which is the point of no return. Any object that crosses the event horizon cannot return. In a very real way, the existence of event horizons is actually quite fortunate because singularities are very unpleasant things to deal with. Since the known physical laws break down at that point, we literally have no idea what goes on there. Having the singularity screened off from the rest of the universe is quite convenient. Physicist Roger Penrose, a close collaborator with Stephen Hawking, even postulated the Cosmic Censorship Hypothesis, which stated that any singularity had to be surrounded by an event horizon. However, it is looking increasingly likely that Dr. Penrose was wrong.

When a massive star nears the end of its life, it starts to contract. When taken in all of its detail, this is an incredibly complex process. Early simulations had to make all kinds of simplifying assumptions: a perfectly spherical star of uniform density with no gas pressure, for example. While the first of those assumptions is fairly reasonable, the latter two are definitely not. The density of a star increases toward the center, and gas pressure definitely does come into play. However, the equations of general relativity are quite complex, so in the absense of computers, they had to do what they could. Given those assumptions, a massive enough collapsing star does indeed form a black hole.

As more computing power became available to model more of the intricacies, a strange phenomenon appeared: there were fleeting moments where the density at a particular point would increase to infinity while the gravity did not rise to the level where it would trap light – in other words, a singularity without an event horizon. In the parlance of physics, a naked singularity. Even stranger, as more and more complex situations were modeled, this happened more and more.

What would a naked singularity look like? In the absence of an event horizon, you could approach arbitrarily close to the singularity and still escape. Infalling matter would be visible all the way to the shining dust-grain of the singularity and would be rocked by intense gravitational shock waves. Effects near the singularity would be somewhat unpredictable, however, because they would be governed by quantum gravity.

By that token, naked singularities could become laboratories for quantum gravity. If a naked singularity were observed, its behavior could give us clues to the shape of a quantum gravity theory. Current quantum gravity theories are suffering from a dearth of observational data to constrain the nearly infinite possibilities. A naked singularity could provide such input. Currently the only place we can look to provide such data is the Big Bang itself.

Some physicists have undertaken simulations of a stellar collapse using loop quantum gravity to see if it would generate observable effects. In loop quantum gravity, space itself is composed of “atoms”, or units of the smallest possible size. It is impossible to put too much matter or energy into too small a space – the result is a tremendous repulsive force generated at that point. In their simulations, that repulsive force dispersed the star and dissolved the singularity. Nearly a quarter of the mass of the star was ejected within the final fraction of a microsecond. To a distant observer, there was a sudden momentary dip in the intensity of radiation from the collapsing star. New instruments scheduled to come on line at the International Space Station in 2013 may have the sensitivity to detect such effects.

Next time, an alternative to dark energy.