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:

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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. | |

Another first order spinor Lagrangian is included. | |

Two paragraphs in Section 4.2.2 are rewritten, and a gap in the argumentation is filled. | |

A new reference on the fall-off properties of self-interacting scalar fields in asymptotically anti-de-Sitter spacetimes is added. | |

The small sphere expression of the Penrose energy in terms of the familiar conformal electric and magnetic parts of the Weyl curvature is given. | |

A reference on the solutions of the Einstein-Yang-Mills equations that are characterized by the vanishing of the Dougan-Mason mass is added. | |

A new paragraph about a new (non-scalar) second order Lagrangian, yielding the trace- action, and the relevant reference are added. | |

A stronger energy positivity result for the Brown-York energy is included, and the reference is given. | |

A stronger energy positivity result for the Kijowski-Liu-Yau energy is added, and the reference is given. | |

A new reference is added. | |

Section 11.3.2 is rewritten. A more detailed discussion of the Dirichlet and Neumann boundary conditions is given and new references are added. | |

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. | |

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. | |

Two references on the existence of averaged trapped surfaces in non-spherically symmetric data sets are added. |

http://www.livingreviews.org/lrr-2004-4 |
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