Sam Collingbourne’s proof of the Gregory-Laflamme instability captures recognition

MELVILLE, N.Y., Aug. 8, 2022 – The Journal of Mathematical Physics, by AIP Publishing, has recognized Sam Collingbourne as the winner of its 2021 Young Researcher Award. His work on the stability properties of spacetimes in high dimensions culminated in the winning publication, “The Gregory-Laflamme instability of the Schwarzschild black string exterior.”

An expert panel of judges selected Collingbourne from a pool of JMP authors, who were all within eight years of receiving their PhD. The prize includes $3,000, and the paper will be highlighted on the journal’s website.

Collingbourne explores solutions to the Einstein equation, which relates the curvature and geometry of spacetime to the matter content in spacetime. The Einstein equation is best thought of as an evolution equation: by specifying some initial conditions, it determines how the data evolves.

The stability of solutions to this equation is one of the main areas of study in general relativity. Collingbourne and others examine what happens when the initial data changes slightly. In four dimensions, the known black hole solutions (in the absence of matter) are expected to be stable. Perturbing the data slightly should still result in the known solution.

In 1993, Ruth Gregory and Raymond Laflamme simulated a 5-dimensional black hole, known as the Schwarzschild black string, showing that the solution to the Einstein equation should be unstable, in stark contrast to the 4-dimensional case. In his winning paper, Collingbourne provides a long-awaited mathematical proof of the existence of this instability.

“By studying the linearized Einstein equation with a certain ansatz, I reduced the problem to showing existence of a solution to a Schrödinger equation for one unknown,” he said. “I established existence of an appropriate solution to this Schrödinger equation with a direct variational argument.”

“It is of particular interest to know whether the black hole structures are stable if disturbed. It has been understood numerically and by an indirect analysis that there is an instability,” said JMP editor-in-chief Jan Solovej. “The significance of the present paper is that it, for the first time, gives a very explicit description of the instability.”

Originally from Edinburgh, Collingbourne studied for an integrated master’s degree in physics at Imperial College London. He fell in love with general relativity, then progressed to obtain a Master of Advanced Study and PhD in mathematics at the University of Cambridge. Beginning in Fall 2022, he will be a Ritt Assistant Professor in the Department of Mathematics at Columbia University.

“The Gregory-Laflamme paper was very special to me. It was my first problem as a Ph.D. student. I loved the problem and learned a lot trying to solve it,” said Collingbourne. “It means a lot that other people appreciated it and thought it worthy of an award!”

**ABOUT THE AWARD**

The Journal of Mathematical Physics Young Researcher Award aims to recognize outstanding research in mathematical physics by a Journal of Mathematical Physics author or coauthors. Candidates for the award must be within 8 years of receiving their doctoral degree, and the award will be given for a paper accepted in the Journal of Mathematical Physics within the previous year.

**ABOUT THE JOURNAL**

Journal of Mathematical Physics publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. See https://aip.scitation.org/journal/jmp.

**ABOUT AIP PUBLISHING**

AIP Publishing is a wholly owned not-for-profit subsidiary of the American Institute of Physics (AIP). AIP Publishing’s mission is to support the charitable, scientific, and educational purposes of AIP through scholarly publishing activities in the fields of the physical and related sciences on its own behalf and on behalf of our publishing partners to help them proactively advance their missions.

For more information:

Wendy Beatty

media@aip.org

301-209-3090