Introduction General Theory of Relativity


The course is taught in English by
Gabriel Martinez-Pinedo, Tel. 06159 71 2750, g.martinez at, Schlossgartenstraße 2, room 304
Ninoy Rahman, Tel. 6159 71 3558, n.rahman at, Schlossgartenstraße 2, room 04

It provides an introduction of the General Theory of Relativity and discusses its main results

Main topics include:

  1. Course description
  2. Preliminaries: Newtonian Gravity, Geometry as Physics, Special Relativity
    • Lecture 2020-11-02: Notes
    • Lecture 2020-11-04: Notes
    • Lecture 2020-11-09: Notes
  3. Gravity as Geometry, Newtonian Gravity in Spacetime Terms: Static Weak Field Metric
  4. Curved spacetimes: Tangent space, vectors and dual vectors (one-forms), Tensors
  5. Motion test particle in curved spacetime: Geodesics, Covariant derivative, Parallel transport
  6. Spacetimes around Spherical Objects and Black Holes: Equations of Motion in Schwarzschild geometry.
    • Lecture 2020-12-07: Notes
    • Lecture 2020-12-14: Notes
  7. Observational tests of General Relativity
  8. Einstein Vacuum Equation: Riemann curvature tensor, Ricci Curvature tensor, Einstein Tensor.
    • Lecture 2021-01-11: Notes
  9. Spherically symmetric vacuum solutions: Schwarzschild geometry.
    • Lecture 2021-01-18: Notes
  10. Einstein Equation with matter: stress-energy tensor
    • Lecture 2021-01-20: Notes
  11. Static spherically symmetric solution: Relativistic stars.
    • Lecture 2021-01-25: Part 1:Notes
  12. Linearized theory of Gravity: Gravitational Waves

Lecture notes (covering item 1 above)


Additional material


The lectures are mainly based on the book (several printings available):
  • James B. Hartle, Gravity: An Introduction to Einstein's General Relativity, Addison Wesley, 1st ed. 2002 (Hardcover)
  • James B. Hartle, Gravity: An Introduction to Einstein's General Relativity, Pearson, 1st ed. 2013 (Paperback)
  • James B. Hartle, Gravity: An Introduction to Einstein's General Relativity, Pearson India, 1st ed. 2014 (Cheap Indian edition, preface and some appendices missing)
  • Supplemental material including Errata, Mathematica Programs and Web Supplements is available at authors website

Some particular deductions are taken from:
  • Bernard Schutz, A First Course in General Relativity, Cambridge University Press, 2nd edition, 2009
Additional bibliography:
  • Sean M. Carroll, Spacetime and Geometry, Cambridge University Press, Cambridge, 2019
  • Robert M. Wald, General Relativity, University of Chicago Press, Chicago, 1984
  • Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, Gravitation, Princeton University Press, 2017
  • Steven Weinberg, Gravitation And Cosmology: Principles And Applications Of The General Theory Of Relativity, Wiley Student Edition, 2008
  • Ray D'Inverno, Introducing Einstein's Relativity, Oxford University Press, 1990