## Admission requirements

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.

## Description

This course provides an introduction to the Theory of General Relativity, with a particular focus on three important astrophysical applications: black holes, gravitational waves 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, a couple of lectures provide 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

4-vectors

Einstein Equation

The equivalence principle and its implications

Motion in curved spacetime and the geodesic equation

Killing vectors

The Schwarzschild geometry

Gravitational redshift

Black holes and the event horizon

Hawking radiation and black hole thermodynamics

Rotation in General relativity: frame dragging

Rotating black holes

Gravitational waves

Cosmology: the Robertson-Walker metric and the Friedmann equation

Flat and spatially curved Universes and their properties

## Course objectives

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, gravitational waves 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:

Abstract thinking

Correctly explaining and analyzing complex and non-intuitive concepts

## Timetable

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

Lectures and problem classes

## Assessment method

Written exam

## Reading list

Gravity. An Introduction to Einstein’s General Relativity, Hartle, ISBN 9781292039145 (*required*)

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Lecturer: Dr. E.M. (Elena) Rossi

## Remarks

**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.