Advanced General Relativity and Quantum field theory in curved spacetimes

 

Syllabus

This is a second term course of the SISSA curriculum in astrophysics & astroparticle physics. The course will consist of 14 lectures of 1h30’ hours each. The aim of the course is to provide advanced knowledge in GR techniques relevant for cosmological problems and in introducing the students to QFT in curved spacetimes.

You can find here the official SISSA web page of the course: Adv.GR.

Textbooks (incomplete list):


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


Warning: I normally use material from papers and lecture notes available from the arXiv. When necessary I’ll tell you where to find this extra material.

Lectures

Subject

Advanced GR

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 definition, Cauchy Horizons, Cosmological Horizons

IX
  • Trapped Surfaces, Trapping Horizons,
  • 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, Unruh effect

XIV
  • Moving Mirrors and Hawking radiation

XV
  • Hawking radiation: Info and Transplanckian problems

XVI
  • Semiclassical gravity, RSET

XVII
  • Semiclassical collapse & BH Entropy interpretations 

XVIII
  • Wormholes, Warp Drives and Time Machines

Exam: There will be one final exam (dates to be fixed) which will take the form of a seminar on a subject of the course chosen by the student and approved by the instructor.

Extra Help: If you need help, get it as soon as possible. As described below, I am always available. Never hesitate to contact your Instructor if you are experiencing difficulties.  

The only way to alleviate a problem is to address it immediately.

I will be available after each lecture, or in my office (SISSA room 507, fifth floor MB) during my weekly office hours or at any other time by appointment (just email me in advance).

Email Me