by E. Tonni (4 credits)
Main topics
General Relativity
- Special relativity and flat space-time
- Manifolds and tensors
- Covariant derivatives and curvature tensors
- Einstein equations and Hilbert action
- Schwarzschild solution and black holes
- Black hole entropy
- Black hole formation
- Fields in curved backgrounds
AdS/CFT
- Basics of CFT
- AdS/CFT correspondence: holographic dictionary
- Witten diagrams
- Bekenstein-Hawking formula and Cardy formula
Holographic Entanglement Entropy
- Entanglement entropy and area law
- Ryu-Takayanagi formula
Holographic Thermalization
- Vaidya backgrounds
Holographic Superconductors
- Minimal setup for holographic superconductors