[ Bern University | Albert Einstein Center for Fundamental Physics | Institute for Theoretical Physics | Gravity and String Theory Group]

Gravity and String Theory Group

Lecture Notes: Matthias Blau

The following Lecture Notes are available (files are gzip-ped postscript files file.ps.gz unless indicated otherwise):

Lecture Notes on General Relativity: [ps.gz file] (1.5 M, 3.9 M after decompression) (also available as a [pdf file] (2.7 M)) (now 550 pages!)
Currently removed for maintenance reasons, sorry! (should be available again by summer 2013)
- Update January 2012:
  - new section on Reissner-Nordstrom
  - new section on de Sitter and anti-de Sitter
  - expanded sections on Schwarzschild (TOV-equation and interior solutions; Painleve-Gullstrand, Lemaitre, Novikov coordinates; surface gravity; overview of other black hole solutions, ...)
  - expanded sections on cosmology (flatness, horizon, cosmological constant problems; more exact solutions, ...)
  - various additions and updates in other sections
- Update February 2012:
  - New section 1.2 on review of Lorentz-covariant formulation of special relativity
  - Expanded section 3.4 on tensor densities
  - New (short) section 21 on Oppenheimer-Snyder solution for collapsing star
  - ADM energy and other minor additions to section 23 on linearised gravity
  - Additions on torsion, non-metricity and Palatini principle in sections 4, 7, and 10
  - discussion of Noether currents, relation between canonical, Belinfante improved and covariant (metric) definitions of energy-momentum tensor etc added to section 10
  - New section 10.5: Comments on Gravitational Energy
- Update August/September 2012 (100+ additional pages):
  - 3 new sections (25, 27,28) on Vaidya Metrics, Radiative Coordinates, Apparent versus Event Horizons, Collapsing Shells etc.
  - related new section on null radial congruences and null Raychaudhuri equation (section 26)
  - expanded section on Killing Vectors and Conserved Charges (now separate section 7)
  - added discussion of Israel (Klösch - Strobl) Coordinates for Schwarzschild (section 15.8)
  - expanded discussion of Oppenheimer-Snyder Collapse (section 23): extrinsic geometry and matching conditions
  - new sections 5.7 and 11.5 on topological couplings and their energy-momentum tensors
  - added section on scalar fields in FRW backgrounds (section 19.5)
  - reorganisation of the lecture notes:
    1. Part I: Towards the Einstein Equations
    2. Part II: Basic Applications of General Relativity
    3. Part III: Selected (Semi-)Advanced Topics)
  - various minor corrections, additions and updates in other sections
- Latest subsequent minor update:
- Further additions and updates to these lecture notes are in preparation.

Some other Lecture notes that I still maintain (and may occasionally update):

Lecture Notes on the Path Integral Approach to Quantum Mechanics: [ps.gz file] (also available as a [pdf file]) (58 pages, 2013). Introductory and elementary lecture notes for part of a Master's course on Advanced Quantum Mechanics.
Lecture Notes on Plane Waves and Penrose Limits: [ps.gz file] (also available as a [pdf file]) (87 pages, 2004). Based on lectures originally given at the 2004 Saalburg/Wolfersdorf Summer School and in various other places.

Some Older Lecture Notes (I no longer maintain since I don't even have the TeX-files anymore):

Symplectic Geometry and Geometric Quantization (47 pages, 1992)
Supergravity Solitons (54 pages, 2002). Lectures given at the Introductory School on String Theory (3 - 14 June 2002). Expanded version of the 1998 and 2000 lectures.

If you have any comments on these notes, complaints, corrections, or constructive criticism, or also if you just happen to find them useful, please let me know.