Thursday 23 June 2016
to 11:00 at
Patrik Lindberg (SU)
The notion of quasi-local mass is examined, speci cally the definitions
suggested by Hawking and Geroch. While these are not fully satisfactory
as de finitions 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 de finitions 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 de finitions 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.