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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.


The classical theory of gravity can be interpreted as the geometry of space-time.It combines the language of field theory with the language of differential geometry onmanifolds. The basic concepts of these subjects will be introduced and it will be shown how they are used to describe gravitational phenomena, from relativistic corrections to orbits of planets and stars, to gravitational waves, black holes and the evolution of the universe at large.


  • Review of newtonian gravity

  • Review of Special Relativity

  • Differential geometry on manifolds, including the concepts of metric, connection and curvature

  • Equivalence principle, geodesic motion

  • Einstein equations, variational principle

  • Gravitational waves

  • Schwarzschild solution, stars and black holes

  • Cosmology of a homogeneous and isotropic universe

Course objectives

This course provides the basis for work in relativistic astronomy, cosmology, quantum gravity and applications. It will :

  • acquaint you with the concepts of field theory and differential geometry

  • teach you to use these concepts to solve problems of gravitational physics and cosmology

  • prepare you for advanced courses on gravitational physics and cosmology

  • allow you to access the scientific literature on these topics and understand the recent progress in experimental and observational research


Physics Schedule
For detailed information go to Timetable in Brightspace

Mode of instruction

Zie Brightspace

Assessment method

A midterm and a final written exam will together determine the grading of the course, the weight of the midterm exam being 40% and of the final exam 60% of the final grade.


Registration for Brightspace occurs via uSis

How to sign up for classes click here

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.A. Achucarro(Ana)