Otherwise invisible (APOD 23 Aug 2008)

[neufer]

http://apod.nasa.gov/apod/ap080823.html

<<Otherwise invisible to telescopic views, the dark matter was mapped by observations of gravitational lensing of background galaxies.>>
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http://www.math.buffalo.edu/mad/PEEPS/p ... .star.html

<<As a boy, Arlie Petters lulled himself to sleep by peering out his window at the swath of stars across the black sky above his small hometown in Belize. The inquisitive youngster constantly peppered his indulgent elders in the Central American village with questions about those alluring, distant lights: "How did they get there? What holds them up? Why do they glimmer so?"

As Petters grew up, he kept that same eager sense of wonderment; today it has led him to revelations about the heavens more stunning than he once dreamed possible. Petters still ponders the heavens, but he now concentrates his talents on a cosmic phenomenon that sounds like the most outlandish science fiction--gravitational lensing. Astronomers first observed gravitational lensing in 1979, when the startled scientists discovered that the image from a distant cosmic object appeared to split into multiple images due to the effect of gravitational force exerted by massive intervening objects between them and Earth.

Unfortunately for astronomers, the universe seldom cooperates by producing simple cosmic phenomena. For one thing, the zigging and zagging of wayward celestial light can be extremely complex because of the gravity of many intervening bodies--like a golf ball putted across the frustrating, undulating green of the seventh hole at the Duke University Golf Course. So, despite the scientific juiciness of gravitational lenses, no mathematician had dared tackle the incredibly thorny problem of creating a general mathematical theory to explain the lens' properties--the theory that would give astrophysicists the right tool to help them analyze the intricacies of wayward cosmic light and deduce what gravitational adventures it had experienced on its way to Earth.

Even Einstein, who first suggested that such lenses might exist, hadn't gone beyond figuring out how a lens would split the light of a single star into two images. Later theorists had gone through laborious calculations to yield only the result that light passing two stars would produce five images. Not until an affable, young, star-struck mathematician from Dangriga, Belize, tackled the problem would there arise the first promising general theory to sort out gravity-warped starlight streaming to Earth.

But that theory and, in fact, Arlie Petters' brilliant career almost didn't happen at all. In the first place, his initial boyhood enthusiasms were for his Methodist religion and art. "I didn't play a lot as a kid," he recalls. "After school I'd come home, do my homework, and then I'd sit at the dining table and draw. That's what I did all the time--draw, draw, draw. Initially, I drew a lot of pictures of nature and people. And then I began drawing more about how I felt, expressing my philosophical feelings by drawing distant horizons and quiet places and mysterious, even mystical settings." His religion and his art, he realized, were connected. "There's a certain joy and peace you get from a belief in God and trying to lead a Christian way of life. And I realized that the good feeling I had in church was similar to this good feeling I got when I look at a beautiful painting or sketch."

The young Arlie did have some inkling that a similar beauty might lie in the world of mathematics. "I had a cousin at home who used to explain a lot of things to me, so I used to bug him a lot. I remember he had books that had these strange symbols that I loved looking at." But when Petters emigrated to the U.S. as a teenager, he fully intended to become a preacher. "Although I did very well in science and math, it was just a side thing," he recalls. As he continued to explore math, though, he experienced the dawning of an intellectual passion. "At first, I didn't know what mathematical thinking was all about. I thought math dealt only with calculations, but as I began looking deeper into math, toward my junior year of high school, I began realizing it has a beauty of its own. And I discovered that the same joy I felt when I did art is present in the abstractions of mathematics."

Mathematician Arlie Petters' theory of gravitational lensing can calculate how the gravitational fields of intervening objects will intricately sculpt the light from a distant cosmic object as it passes them on its way to Earth. These three computer diagrams plot the "caustics" produced by different arrays of such intervening objects. Caustics are positions in space where a distant object's image would be gravitationally focused by an array of intervening objects, down to intensely bright points called singularities.

The adventure confirmed Petters' fascination with mathematics, and his brilliance as a student brought him yet another golden opportunity: a Bell Labs Fellowship to study math at one of the world's meccas of math and astronomy, M.I.T. There, he learned both math and humility. "I left Hunter College as a star, but when I arrived at M.I.T., I was just average," he says with a chuckle. The sobering experience led him to serious soul-searching to assess his talents realistically and seek a specialization to match them. "I discovered that my mathematical thinking is much stronger than my physical thinking. And so I anchored myself in math and looked out across physics."

Following his instinct, he spent his last two years of graduate work at Princeton and it was there--working under renowned astrophysicist David Spergel--that he first learned about the startling observations of gravitational lenses. "It sounded exciting to me, like getting a chance to be on the frontier, clearing undeveloped land," he says. So, Petters plunged into the physics and mathematics of the lenses, seeking to stake his own claim in this new intellectual landscape. "Initially, it was tough trying to get through some of the actual physics literature because they looked at gravitational lensing strictly from a physics perspective. And I was trying to dig out the underlying mathematics of the subject."

Then, on a train ride back to M.I.T. to see his math adviser Bertram Kostant--as he watched the New England landscape slide past the train window and mulled, he says, over the complexities of gravitational lenses--he experienced the conceptual Eureka! that would propel his professional career. "The problem of how to describe gravitational lenses mathematically had stuck in the back of my head," he says. He knew that other attempts to create theories about them had involved "a lot of algebra, a little calculus, and a whole lot of messy, messy calculations." Suddenly, he says, he realized that the tools for creating such a theory already existed, in a sophisticated kind of mathematics called singularity theory. Ironically, a special case of this theory, called Morse theory, had existed even in Einstein's day, and the legendary scientist could have used it to create a lensing theory, had he thought of it.

Inspired by his train-ride flash of insight, Petters launched himself on an effort to use singularity theory to build the first general mathematical theory of gravitational lensing. The payoff was immediate. His work revealed key details of how gravity from not just one or two objects but multiple objects at various cosmic distances will split passing light into images, including their number and magnification. It also allowed him to begin to map an optical "halo" phenomenon that occurs, for example, when a distant star lies directly behind an intervening object. In such rare instances, gravitational lensing causes the star's image to appear as a ring of intense brightness surrounding the object. Astrophysicists use the term "caustics" to describe the unique positions of distant stars or quasars that produce these infinitely bright points.

Advancing his work far beyond a single source and single lens, Petters has now used singularity theory to predict the caustics that result when the gravity of many objects--galaxies, black holes, and stars--sculpt starlight on its cosmic journey. "It turns out that when you have more than one intervening star, the caustics are no longer a point," he explains. "They form curves."

Remarkably beautiful curves, in fact. With a powerful computer, astrophysicists and mathematicians have used Petters' theory to generate intricate maps of such caustics, caused not only by the gravity of multiple objects such as stars but also by objects in different planes--each intensifying or attenuating the light refracted from the other. "My dream has been to isolate those properties of gravitational lensing that are generic and stable--features that are robust and independent of the simplifications used in most models of real lens systems," he says. "Singularity theory gives me a rigorous framework for accomplishing this goal, yielding insights where physical intuition can hardly penetrate.">>
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http://en.wikipedia.org/wiki/Arlie_Petters

<<Arlie Petters is a pioneer in the research of Gravitational Lensing and developed the mathematical theory of lensing over the ten year period from 1991-2001. His research has been used in predicting the nature of space time near black holes and developing new ways to test hyperspace gravity models and Einstein’s General Relativity theory.

Arlie Petters (born February 8, 1964 in Dangriga) is a Belizean American physicist and mathematics professor at Duke University. During his impoverished childhood in the Central American country of Belize he developed a passion for learning and especially science. In 1979 he emigrated to the United States and became a Citizen in 1990. He received his B.A and M.A at Hunter College in Mathematics and Physics and completed his PhD in Pure Mathematics at MIT. Petters served as an instructor in pure mathematics at MIT from 1991 to 1993 and was an assistant Professor of Mathematics at Princeton University from 1993 to 1998. In 1998 he joined Duke University and became the first black tenured faculty member in the Mathematics and Science department, and as of 2003 he is a full Professor. He has received an honorary PhD from Hunter College in 2008.>>
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[bystander]

Wow, Arlie obviously does not subscribe to the Peter Principle. Can Arlie's math be used to map "Dark Matter" by observing the lensing it produces?