Research Interests for M. George Lam

I study curvature in general relativity under Dr Hubert Bray. Recently I have been investigating the question of defining mass in a spacetime. The mass of an entire spacetime have been studied extensively over the past few decades with many fundamentals results, two of which are the Positive Mass Theorem and the Penrose Inequality. On the other hand, the question "How much matter is in a given region of a spacetime?" is still very much an open problem. Various definitions of this so called quasi-local mass have been proposed, but none satisfies all the desirable properties one would expect in such a definition.

Besides being interesting in their own rights, such quasi-local mass functions have turned out to be important tools in understanding the geometry of spacetime. Husiken and Illamen proved the Riemannian Penrose Inequality for a single black hole via inverse mean curvature flow and the Hakwing mass, and Bray used the conformal mass to prove case with any number of black holes. More recently, Shi and Tam obtained lower bounds for the Brown-York mass and the Bartnik mass for compact three manifolds with smooth boundaries and derived sufficient conditions for the existence of horizons for a certain class of compact manifolds as a consequence. All these lead to the idea that a 'good' definition of quasi-local mass should also provide us with insights into the general structure of spacetime.