Living Reviews in Relativity

"Isolated and Dynamical Horizons and Their Applications"
Abhay Ashtekar and Badri Krishnan  

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1 Introduction
2 Basic Notions
2.1 Isolated horizons
2.2 Dynamical horizons
3 Area Increase Law
3.1 Preliminaries
3.2 Area increase law
3.3 Energy flux due to gravitational waves
4 Black Hole Mechanics
4.1 Mechanics of weakly isolated horizons
4.2 Mechanics of dynamical horizons
4.3 Passage of dynamical horizons to equilibrium
5 Applications in Numerical Relativity
5.1 Numerical computation of black hole mass and angular momentum
5.2 Initial data
5.3 Black hole multipole moments
5.4 Waveform extraction
6 Applications in Mathematical Physics
6.1 Beyond Einstein–Maxwell theory
6.2 Structure of colored, static black holes
7 Applications in Quantum Gravity
7.1 Preliminaries
7.2 Quantum horizon geometry
7.3 Entropy
8 Outlook
9 Acknowledgements
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