While for most people a hot cup of coffee is a reason to get up in the morning, for some scientists it holds the clue to understanding how black holes work and also represents a way of finding the elusive dark matter. A Duke University professor and one of his graduate students realized that the way in which light and shades interacted in coffee ripples were very similar to the way gravity magnified and distorted light coming from very distant galaxies.

They derived a principle out of their observations, and announced that the violation of this principles could be the first step towards developing a new way of looking for the mysterious dark matter. This form of matter has thus far remained only theoretical, but physicists say that the goal of finding it is drawing nearer with each passing year. Duke Professor of Mathematics, Physics and Business Administration Arlie Petters shares that the find makes use of some properties that light has, of bending when it hits curved surfaces, a concept mathematicians and physicists refer to as a “cusp curve.”

In such circumstances, light bends to an ivy leaf-shaped pattern, which has a point in the center and very bright sides. Such a bright edge is called “caustic,” taking after an alternative dictionary definition of the word, which lists “burning bright” next to the other entries. “It happens because a lot of light rays can pile up along curves,” Petters tells. “Mother Nature has to be creating these things. It's amazing how what we can see in a coffee cup extends into a mathematical theorem with effects in the cosmos.”

“As with any illumination pattern, some areas will be brighter than others. And the brightest parts will be along these caustic curves,” he adds. When observed from the Earth, the entire Universe looks like an ever-interacting chaos of gravity and light, whose roots can be traced back and identified in the space-time continuum. Already, team members who process data coming in from observatories and telescopes need to be aware of the fact that errors in the lenses themselves have to be compensated for. A dot of light can reflect in an imperfect mirror or lens in peculiar ways and create other reflections of itself, which could have astronomers scratching their heads for decades to come.

In a study published in the March 23rd issue of the Journal of Mathematical Physics, Petters and graduate student Amir Aazami extend theoretical examples of light caustic curves to cover what the expert termed “caustic metamorphosis,” changes which might occur over space-time, between varying amounts of light and gravity.

Talking about specific types of light reflection in telescopes' lenses, Petters maintains that, “For one of the higher order caustics, if there are two pairs of lensed images that are close to each other but not equally bright, then the theorem is violated. The reason would be some substructure in the galaxy.” Usually, he points out, such images are equal in both size and brightness, and are created by certain light patterns and types of mirrors or lenses on modern telescopes.

The “substructure” that could be detected via this method may very well be the elusive dark matter, the expert mentions. It wouldn't allow astronomers to actually assess many of its properties, but its movements would at least become visible to a certain extent.