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 [269

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 Other inequalities
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
13.5 Quasi-local radiative modes of general relativity
13.6 Potential applications in cosmology

13 Applications in General Relativity