course dates credits
Advanced GR and QFT in Curved Spacetimes Jan 13 - Mar 5 5
teachers schedule term
Stefano Liberati Tue and Thu, 11:30-13:00 2

Program:

    Advanced GR:
    1. Foundations, axiomatic derivation of Local Lorentz invariance, Equivalence principle formulations
    2. Elements of differential geometry
    3. Curved Manifolds and sub-manifolds
    4. Spacetime symmetries and conserved quantities
    5. Spacetime kinematics: Geodesic deviation equation, Raychauduri equation, Energy Conditions
    6. Spacetime dynamics: Lagrangian formulation of General Relativity
    7. Alternative theories of gravitation
    8. Global methods: Carter Penrose diagrams, Singularities and event horizons
    9. Stationary horizons: Killing Horizons, Surface Gravity, Cauchy Horizons, Cosmic Censorship
    10. Dynamical horizons: Cosmological Horizons, Trapped Surfaces, Trapping Horizons
    11. Singularity theorems and regular black holes
    12. From Kerr Black Holes to Black Hole Mechanics: Kerr metric, Penrose process, Superradiance
    13. Intermezzo: More on hypersurfaces, Hamiltonian formulation of GR, ADM mass and angular momentum
    14. From Black Hole Mechanics to black hole Thermodynamics
    Quantum Field Theory in Curved Spacetimes:
    1. Introduction to Quantum Field Theory in Curved Spacetimes
    2. Casimir Effect, Unruh effect
    3. From moving mirrors to evaporating black holes
    4. Open issues with Hawking radiation: Transplanckian and Info Loss problems, black hole entropy interpretations
    5. Semiclassical gravity: Renormalized Stress Energy Tensor, semiclassical collapse
    6. Time Machines and Chronology Protection

Prerequisites:

An introductory course to GR

Books:

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:

Filename Size (bytes) Date Modified
Adv.GR-QFTinCS-Lect.Notes.pdf 6.86 MB Mar 6 2026 8:44 PM
SyllabusAdvGR2026.pdf 157.13 KB Jul 9 2025 10:36 AM