Change Log

Fast-track revision published on 01 Jun 2005

Global description:

Recent developments of the field are included. 16 new references are added, minor improvements and corrections of the text are made at several points, and the bibliography is updated. The major changes are as follows:

Changes in detail:

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Update Icon The discussion is changed, and a new paragraph is added. A new, quasi-local version of the holographic hypothesis is formulated, and it is explained how it works for physically important classical matter fields in Minkowski spacetime. Two references are added.
Update Icon Another first order spinor Lagrangian is included.
Update Icon Two paragraphs in Section 4.2.2 are rewritten, and a gap in the argumentation is filled.
Update Icon A new reference on the fall-off properties of self-interacting scalar fields in asymptotically anti-de-Sitter spacetimes is added.
Update Icon The small sphere expression of the Penrose energy in terms of the familiar conformal electric and magnetic parts of the Weyl curvature is given.
Update Icon A reference on the solutions of the Einstein-Yang-Mills equations that are characterized by the vanishing of the Dougan-Mason mass is added.
Update Icon A new paragraph about a new (non-scalar) second order Lagrangian, yielding the trace-x action, and the relevant reference are added.
Update Icon A stronger energy positivity result for the Brown-York energy is included, and the reference is given.
Update Icon A stronger energy positivity result for the Kijowski-Liu-Yau energy is added, and the reference is given.
Update Icon A new reference is added.
Update Icon Section 11.3.2 is rewritten. A more detailed discussion of the Dirichlet and Neumann boundary conditions is given and new references are added.
Update Icon A new section (Section 11.3.3 in the new version) is opened for a part of the former Section 11.3.2 and for the recent ‘main extrinsic curvature masses’. A new reference is added.
Update Icon A recent counter-example to the apparent horizon version of the Penrose inequality for non-time-symmetric data sets is mentioned, the discussion is improved and a reference is added.
Update Icon Two references on the existence of averaged trapped surfaces in non-spherically symmetric data sets are added.