13 Applications in General Relativity

In this section we give a very short review of some of the potential applications of the paradigm of quasi-locality in general relativity. This part of the review is far from complete, and our aim here is not to discuss the problems considered in detail, but rather to give a collection of problems that are (effectively or potentially) related to quasi-local ideas, tools, notions, etc. In some of these problems the various quasi-local expressions and techniques have been used successfully, but others may provide new and promising areas for their application. For a recent review of the applications of these ideas, especially in black hole physics, with an extended bibliography, see [294Jump To The Next Citation Point, 293].

 13.1 Calculation of tidal heating
 13.2 Geometric inequalities for black holes
  13.2.1 On the Penrose inequality
  13.2.2 On the hoop conjecture
  13.2.3 On the Dain inequality
 13.3 Quasi-local laws of black hole dynamics
  13.3.1 Quasi-local thermodynamics of black holes
  13.3.2 On isolated and dynamic horizons
 13.4 Entropy bounds
  13.4.1 On Bekenstein’s bounds for the entropy
  13.4.2 On the holographic hypothesis
  13.4.3 Entropy bounds of Abreu and Visser for uncollapsed bodies
 13.5 Quasi-local radiative modes of general relativity
 13.6 Potential applications in cosmology

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