In this talk, I will show how basic techniques from differential geometry
are applied in the research of general relativity. Specifically, I am going
to examine the behavior of a model of the ``quasi-local energy'' of the
gravitational field, recently proposed by Liu and Yau, near a point and near
the null infinity in a 4-Lorentzian manifold. Some preliminary results of
potential interest to physicists will be presented but the focus of the talk
will be on the underlying geometry.
A tentative list of topics that will be discussed in the talk:
- normal neighborhood on the null cone of a point
- orthornormal null moving frames adapted to a space-like submanifold
- isometric embedding of a closed space-like orientable 2-surface into a
Lorentzian manifold
- asymptotic structure of a Lorentzian manifold at null infinity
- gravitational radiation (mass loss and energy flux)
References:
-
Liu, C.-C. M. and Yau, S. T., Phys. Rev. Lett. 90, 231102 (2003)
- Liu, C.-C. M. and Yau, S. T., J. Amer. Math. Soc. 19, 181-204 (2005)
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