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Theory of General Relativity


Admission Requirements

BSc physics, BSc astronomy, BSc mathematics. This course assumes working knowledge of Newtonian gravity and Special Relativity, including familiarity with Minkowski diagrams and the use of the Einstein summation convention. These topics will not be reviewed in this course. An introductory bachelor course in gravity such as the "Astronomica Relativity" course 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 on manifolds. 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.


  • Equivalence principle, geodesic motion

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

  • Symmetries and Killing vectores

  • Einstein equations, variational principle

  • Schwarzschild solution, stars and black holes

  • Cosmology of a homogeneous and isotropic universe

  • Gravitational waves

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

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

Mode of instruction

See Brightspace

Assessment method

To be discussed with the students a few weeks into the course. Typically a final written exam determines the grade of the course, but there are options for a more continuous form of assessment that can influence the final grade. These may include a midterm exam or a group project or both.

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


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.

Extensive FAQ's on MyStudymap can be found here.


Lecturer: Prof.dr.A. Achucarro (Ana)