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 [294, 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

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

Living Rev. Relativity 12, (2009), 4
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