Course Dates Credits
Advanced GR and QFT in Curved Spacetimes Jan 16 - Mar 15 14
Stefano Liberati


I Foundations, axiomatic derivation of Local Lorentz invariance, EP
II Manifolds, Curvature, Intrinsic vs Extrinsic curvature
III Lie Derivative, Killing vectors
IV "Geodesic deviation eq., Raychauduri eq., En. Conditions"
V Lagrangian Formulation and Action principle for GR (metric+Palatini)
VI Alternative Gravitation theories
VII Global methods – Carter Penrose diagrams - BH theory: singularities and event horizons.
VIII Killing Horizons - Surface Gravity
IX Singularity theorems
X Kerr BH and the Penrose process
XI From BH mechanics to BH Thermodynamics QFT in Curved Spacetime
XII QFT in CS intro
XIII Casimir effect, Cosmological particle production, Unruh effect
XIV Moving Mirrors and Hawking radiation
XV Hawking radiation: Info and Transplanckian problems
XVI Semiclassical gravity, RSET
XVII Semiclassical collapse
XVIII Wormholes, Warp Drives and Time Machines


Having allowed an introductory course to GR


Advanced GR:
“General Relativity”, R.M. Wald,
“Spacetime and Geometry”, S.Carrol,
“A relativist toolkit”, E. Poisson.

QFT in curved spacetime:
“Quantum fields in curved space”, N.C. Birrell & P.C.W. Davies,
“Vacuum effects in strong fields”, A.A. Grib, S.G. Mamayev, V.M. Mostepanenko,
“Introduction to quantum effects in Gravity”, V.F. Mukhanov and S. Winitzki.

Online Resources:

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