Knowledge of calculus and linear algebra at bachelor's level is required, as well as special relativity, and of classical mechanics, including its Lagrangian formulation. In terms of the Leiden curriculum, the student must have successfully completed the first year, and in addition must have successfully completed the courses Classical Mechanics b and Lineaire Algebra 2 or Lineaire Algebra 2NA. Without this full set of prerequisites, enrolment will not be allowed.
This course provides an introduction to the Theory of General Relativity, with a particular focus on two important astrophysical applications: black holes and the evolution of the Universe.
The first part of the course introduces in several lectures the theory of General Relativity. Following that, three key physical applications are discussed. First, the physics of black holes is covered in several lectures. Then, one lecture provides an introduction to gravitational waves. Finally, in several lectures, the application of General Relativity to the Universe as a whole, including its origin and evolution, is introduced.
The course sidesteps the usual mathematical approach to the subject (based on tensor calculus), and instead starts from the metric as the central concept. The course uses a textbook following the same approach.
The following themes are covered:
Review of Special Relativity
The equivalence principle and its implications
Motion in curved spacetime and the geodesic equation
The Schwarzschild geometry
Black holes and the event horizon
Hawking radiation and black hole thermodynamics
Rotation in General relativity: frame dragging
Rotating black holes
Cosmology: the Robertson-Walker metric and the Friedmann equation
Flat and spatially curved Universes and their properties
Principal course objective: upon completion of this course you will be able to explain the fundamental tenets of General Relativity, their implications for the nature of space, time and gravity, and will be able to carry out basic calculations in relation to black holes and the Universe as a whole.
Upon completion of this course you will be able to:
Explain the fundamental principles of General Relativity
Calculate the motion of particles in any curved spacetime
Explain the properties of non-rotating and rotating black holes
Analyze the motion of particles in the vicinity of black hole horizons
Explain Hawking radiation and its relation to black hole thermodynamics
Explain the dragging of inertial reference frames by rotating masses in General Relativity
Explain the nature and properties of gravitational waves
Calculate simple physical parameters from gravitational wave experiments
Calculate physical quantities in a dynamic Universe
Explain and quantitatively predict the evolution of model Universes
At the end of this course, you will have been trained in the following behaviour-oriented skills:
Correctly explaining and analyzing complex and non-intuitive concepts
See Schedules bachelor Astronomy
Mode of instruction
Lectures and problem classes
Written exam, see Examination schedules bachelor Astronomy
Blackboard will be used to communicate with students and to share lecture slides, homework assignments, and any extra materials. You must enroll on Blackboard before the first lecture. To have access, you need a student ULCN account.
Gravity. An Introduction to Einstein’s General Relativity, Hartle, ISBN 9781292039145 (required)
Register via uSis. More information about signing up for classes and exams can be found here. Exchange and Study Abroad students, please see the Prospective students website for information on how to register. For a la carte and contract registration, please see the dedicated section on the Prospective students website.
Lecturer: Dr. E.M. (Elena) Rossi
Assistants: Orlin Koop, Hidde Jense