Description
Chapter I: INTRODUCTION 1. A brief review on essentials of General Relativity, from basic concepts, mathematical framework and Einstein equations Einstein-Hilbert action and classical tests of GR; 2. Brief review of history and timeline of developments from Schwarzschild solution to black hole mergers and to information paradox and rewall; 3. Gravitational collapse and Chandrasekhar mass bound; 4. Different schools of thought on black holes: high energy oriented, GR oriented and quantum information theory oriented; open issue how to merge these schools Chapter II: BASIC CONCEPTS and TOOLS 1. Schwarzschild metric and some basic facts and analysis; 2. Analysis of geodesics, notion of Killing horizon and near horizon Rindler geometry; 3. Kruskal coordinates, maximal extensions and Carter-Penrose diagram; 4. Einstein-Maxwell theory and Reisner-Nordstrm solution and its basic analysis; 5. Kerr solution and its basic analysis; 6. Black holes in (A)dS backgrounds. Chapter III: CLASSICAL ASPECTS 1. Lensing and black hole shadows; 2. Super-radiance, Penrose process and black hole mining; 3. Gravitational wave emission in black hole mergers; 4. Accretion disk physics; 5. Extremal black holes, their near horizon and basic analysis. Chapter IV: ADVANCED CONCEPTS 1. Mathematical defnition of black holes, notion of various different horizons, Killing, event, cosmological, isolated; trapped surface. 2. Conjectures and theorems (Cosmic censorship; Penrose mass inequality, singularity, uniqueness and topology theorems) 3. Raychaudhuri equation and area theorem (2nd law); energy conditions; 4. Linear and nonlinear stability of black hole solutions; 5. More detailed analysis of collapse, Choptuik exponents and critical exponents; 6. Canonical boundary charges (1st law), ADM, Brown-York, Regge-Teitelboim, Iyer-Wald-Zoupas, Barnich-Brandt and Hajian-Sh-J charges. 7. Variation principle; Gibbons-Hawking-York boundary term; Brown-York stress tensor; 8. Quasi-normal modes and black hole perturbations; 9. Four laws of black hole thermodynamics and their new derivations a la Wald-Hajian-Sh-J; Chapter V: SEMICLASSICAL ASPECTS 1. Quantization on black hole backgrounds; 2. Unruh effect; 3. Hawking effect; 4. Bekenstein entropy and the area law, the Bekenstein bound; 5. Parikh-Wilczek tunneling; 6. Black hole evaporation; 7. Membrane paradigm. Chapter VI: EXPERT TOPICS 1. Gravity in lower dimensions (including various asymptotic symmetry algebras) 2. Gravity in higher dimensions (including a brief discussion on supergravity); 3. Higher dimensional black hole/ring/brane solutions. 4. Aspects of holography – holographic renormalization, correlation functions and asymptotic symmetries 5. Extremal black holes and attractor mechanism 6. Kerr/CFT and related topics 7. Soft hair and black hole microstates. Chapter VII: QUANTUM ASPECTS 1. Black holes in string theory; 2. Microstate counting; 3. Microstate identification/constructions, fuzzballs, fluffballs; 4. Information paradox and black hole complementarity and firewalls; 5. Black holes and quantum gravity; 6. Information paradox and the AdS/CFT; 7. Holography, Quantum information (entanglement entropy, Bousso bound, QNEC etc.) and generalized laws of black hole thermodynamics. Chapter VIII: OUTLOOK 1. Summary; 2. Outlook and open issues; – Experimental/observational prospects – Black holes as a window to Quantum Gravity – gravity may be emergent | what does it emerge from? Chapter IX: SOLUTIONS TO EXERCISES We present numerous exercises throughout the book and in this chapter we give solutions to a selected subset of them. Appendices We intend to have some appendices in which we present some details of crucial mathematical frameworks and formulations not fitting into the main text, in particular – Cartan formulation – Basics of QFT in curved spacetime – Covariant phase space method
