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Theory of General Relativity


Admission Requirements

BSc physics, BSc astronomy, BSc mathematics. An introductory bachelor course in gravity such as the "Introduction to general relativity and astrophysical applications" offered in Leiden is strongly recommended.


This course is an introduction to the modern theory of classical gravity. Generalizing from special relativity, we show the need for and will develop the formalism of differential geometry in some depth. This will allow us to study the motion of particles and fields in a gravitational field as motion through a curved spacetime. In turn this leads to the introduction of the Einstein field equations for the dynamics of the spacetime itself. Using these insights, we will study a variety of important physical consequences and applications, i.e. relativistic corrections to the Newtonian gravity, relativistic stars, gravitational waves, black holes and spacetime singularities, relativistic Big Bang cosmology.

Course objectives


  • Manifolds, (co)tangent spaces , tensor calculus.

  • Special relativity, the energy-stress tensor and causality.

  • Differential geometry: parallel transport, covariant derivatives and geodesics.

  • Riemannian geometry: curved manifolds and curvature invariants.

  • Einstein’s General Theory of Relativity

  • The Schwarzschild solution and simple black holes

  • Linearized gravity and gravitational waves

  • Friedmann-Robertson-Walker Cosmology


Physics Schedule

Mode of instruction

Lectures and home work assignments. Sessions will be ofered to ask questions about the homework a couple of days before they are due.

Assessment method

Homework assignments (60%) and a written final exam (40%). A pass on the final exam is required. There is a possibility to retake the exam. The date for the retake will be decided after consulation.


Course material is on Blackboard.
To have access to Blackboard you need a ULCN-account.Blackboard UL

Reading list

Primary text book:
S. Carroll, Spacetime and Geometry, an Introduction to General Relativity (Benjamin Cummings, 2003). Recommended background reading:
J.B. Hartle, an introduction to Einstein's general relativity, (Addison-Wesley, 2003). A bachelor level introductory text stressing the physical concepts.
R. Wald, General Relativity (Univ. Chicago Press, 1984). High level treatise of the relevant differential geometry.
C. Misner, K. Thorne, J.A. Wheeler, Gravitation (Freeman, 1973). Standard text on the professional level .


Lecturer: Prof.dr.J. Zaanen (Jan)