Washington, April 15 (ANI): A Duke University professor and his graduate student have discovered a universal principle that unites the curious interplay of light and shadow on the surface of your morning coffee with the way gravity magnifies and distorts light from distant galaxies.
According to the researchers, scientists will be able to use violations of this principle to map unseen clumps of dark matter in the universe.
Light rays naturally reflect off a curve like the inside surface of a coffee cup in a curving, ivy leaf pattern that comes to a point in the center and is brightest along its edge.
Mathematicians and physicists call that shape a "cusp curve," and they call the bright edge a "caustic," based on an alternative dictionary definition meaning "burning bright," explained Arlie Petters, a Duke professor of mathematics, physics and business administration.
"It happens because a lot of light rays can pile up along curves," he added.
Caustics show up in gravitational lensing, a phenomenon caused by galaxies so massive that their gravity bends and distorts light from more distant galaxies.
"It turns out that their gravity is so powerful that some light rays are also going to pile up along curves," said Petters, a gravitational lensing expert.
"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," he added.
From the vantage point of Earth, the entire cosmos looks like a vast interplay of gravity and light that can extend far back into spacetime.
"As with any illumination pattern, some areas will be brighter than others. And the brightest parts will be along these caustic curves," Petters said.
Petters and graduate student Amir Aazami extended the mathematics of relatively simple examples to include what Petters called "higher order caustics."
In such situations, the interplay of light and gravity may extend further into spacetime and undergo various forms of "caustic metamorphosis" in the process.
Aazami was informally testing out a special case of their evolving caustics theorem called an "ellyptic umbilic" by using a technical computing software program when he noticed a pattern.
Petters realized Aazami had found a universal mathematical principle so pervasive that it can impose balance on the most complicated gravitational lensing illusions.
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," Petters said, likely dark matter near one of the images that causes it to be demagnified. (ANI)