A black hole is a region of space with such intense gravity that nothing, not even light, can escape. Many collapsed stars are thought to be black holes.

Physicist Stephen Hawking shocked experts in the seventies by showing that these objects are not completely black. According to Hawking, they radiate away energy and mass very slowly.

Since then, physicists have struggled to solve the difficult equations that describe the evolution of a black hole as its mass dwindles over time.

Ring found if he assumed the radiation rate was constant, and he divided the space around the black hole in a special way into a near region, close to the event horizon, and a far region, where the radiation is outgoing, he could solve the equations explicitly.

"Some interesting theorems were known using near and far regions and a boundary that would shrink as the black hole got smaller," said Ring, who studied Physics at the California Institute of Technology and Texas A&M University. "But it was a surprise that a constant radius boundary would make an explicit solution possible."

For a black hole formed by collapse of a star, Ring's approximation will be good for around 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years. For comparison, the age of the universe is thought to be around 13,700,000,000 years.

"Ideally we would like to model the end of a black hole's life" Ring said. "This is especially difficult since the curvature of space-time is so severe that quantum gravity effects become important."

Ring hopes his experience and success as an amateur physicist will keep young people interested in physics.

"Many young people get excited about understanding the origins of the universe and the way nature works at its most fundamental level, but they find career opportunities are very limited," Ring said.

"There are no practical applications for these ideas, and it's difficult to find an organization willing to provide resources for study, but that does not mean amateurs have no future in physics. An amateur can still make an important contribution," he added.

Ring explains his model in detail in his article "A Linear Approximation to Black Hole Evaporation," scheduled to appear in the Aug. 7 issue of the journal Classical and Quantum Gravity.

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