The limiting behavior of the Liu-Yau quasi-local energy

Peng Peng Yu

Dartmouth Physics Department

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:

  1. normal neighborhood on the null cone of a point
  2. orthornormal null moving frames adapted to a space-like submanifold
  3. isometric embedding of a closed space-like orientable 2-surface into a Lorentzian manifold
  4. asymptotic structure of a Lorentzian manifold at null infinity
  5. gravitational radiation (mass loss and energy flux)

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