Thesis defense

Quasi-local mass

by Patrik Lindberg (SU)

Europe/Stockholm
C5:1007

C5:1007

Description
The notion of quasi-local mass is examined, specically the definitions suggested by Hawking and Geroch. While these are not fully satisfactory as definitions of quasi-local mass, they have nevertheless proven to be useful tools, for example in proving the positivity of the ADM mass and a version of the Penrose inequality. The mass definitions are evaluated in various special cases, demonstrating explicitly that they can become negative for some very simple surfaces. For a few special spacetimes, a class of surfaces is identified for which the Hawking mass makes sense. Corrections are made to both definitions in the presence of a non-zero cosmological constant. Furthermore, the monotonicity of the Geroch mass under the inverse mean curvature flow (IMCF) is studied in detail, including a numerical evaluation of the evolution of a spheroid.