Robert Bartnik

Bartnik died in 2022. A visiting fellowship programme at Monash University bears his name.

Research His work with John McKinnon has been widely studied in the physics literature. They show that there is a discrete set of static solutions to the coupled Einstein/Yang-Mills equations which are geodesically complete and asymptotically flat. This is interesting since such solutions are known not to exist in the cases of the Einstein vacuum equations, the coupled Einstein/Maxwell equations, and the Yang-Mills equations. Although Bartnik and McKinnon's work was numerical, their observed phenomena has been mathematically justified by Joel Smoller, Arthur Wasserman, Shing-Tung Yau, and Joel McLeod.

In the mathematics literature, he was known for his work with Leon Simon on solving the Dirichlet problem for prescribed mean curvature, in the setting of spacelike hypersurfaces of Minkowski space. His most widely cited work is on the geometric and analytic study of the ADM mass. He showed that it is geometrically defined by constructing "optimal" asymptotically flat coordinates, and gives an extension of Edward Witten's proof of the time-symmetric positive energy theorem to the higher-dimensional spin setting.

Major publications As of 2022, Bartnik had been the author of around 30 research articles. The following publications are among the best-known: