Admission requirements
None.
Description
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.
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 "Astronomical Relativity" course offered in Leiden is strongly recommended.
Topics:
Equivalence principle, geodesic motion;
Differential geometry on manifolds, including the concepts of metric, connection and curvature;
Symmetries and Killing vectors;
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.
Schedule
The timetables are available through My Timetable (see the button in the upper right corner).
Teaching method
The course combines lectures and explanations, on the blackboard, with problem solving where students work in groups and can receive personal attention. Often these happen during the same session. The emphasis is on asking questions and on self-study. The sessions are not streamed or recorded. Internet resources and LLMs are both welcome and scrutinized.
For more information see Brightspace
Assesment method
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. To be discussed with the students a few weeks into the course.
The final grade will be determined as follows:
- Final exam (100%)
Resit, review & feedback
Examinations are held twice during the academic year for each component offered in that academic year. Midterm tests cannot be retaken. The Board of Examiners determines the manner of resit for practical assignments.
For review and feedback, see Brightspace.
Reading list
Primary text book:
- S. Carroll, Spacetime and Geometry, an Introduction to General Relativity (Benjamin Cummings, 2003). The book was reprinted without changes by Cambridge University Press in 2019.
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
Registration
Enrolment through MyStudyMap (button in upper right corner) is mandatory. General information about course and exam enrolment is available on the website.
Contact
For substantive questions, contact the lecturer(s) (listed in the right information bar).
Remarks
The sessions are not streamed or recorded.
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.