The classical view of a black hole is that it is an object so massive that nothing, not even light, can escape its pull. In 1974, Stephen Hawking put forth his idea that black holes are not technically black—they emit radiation and evaporate over time. Hawking radiation was assumed to be described by ideal black body radiation, and this assumption allowed for the derivation of the temperature and entropy of a black hole. But we don't actually know how black a black hole is or, in more scientific terms, what are the bounds of the effects of greybody terms in a black hole's radiation spectrum?

In a paper set to be published in an upcoming edition of Physical Review Letters a pair of New Zealand mathematicians, Petarpa Boonserm and Matt Viser, attempt to put realistic bounds on the magnitude of these greybody terms. Previous attempts to solve this problem, according to the authors, have used "various approximations that move one away from the physically most important regions of parameter space." Basically, that means, in the authors' view, that past efforts have relied on assumptions that have moved the solutions away from important real world cases.

The duo attempt to rigorously solve for bounds on the transmission probabilities for waves moving through the region of space outside of a Schwarzschild black hole—Schwarzschild black holes are the simplest type, one that is described as a spherically symmetric body with no charge or angular momentum. The pair derived upper and lower bounds for various cases and came up with closed-form analytical expressions that are functions of the radiation frequency and mass of the black hole alone.

An important point to note here is that the work wasn't an attempt to get an ultimate answer regarding black holes; rather, the pair attempt to use assumptions that don't make the work easy, but rather those that keep the results closer to reality. This put a direct answer out of reach, but did allow them to identify limits to how large or small these effects should be.

An interesting side effect of the resulting greybody terms in the radiation spectrum is that certain objects will "bounce" off a black hole. As is typical in the physical world, this oddity, which goes against common sense, is confined to the quantum world. If you throw your iPod into a black hole, it's gone for good. However, if you have a quantum object with the appropriate energy, it can have a non-zero probability of bouncing off due to these greybody terms. High energy quantum objects will have a near zero bounce but this work suggests that, at low energies, the bounce has the potential to be quite large. Yet another phenomenon to add to the long list of oddities that exist in the quantum world.

Physical Review Letters, 2008. Upcoming (arXiv link)