## 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 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
- 4-vectors
- 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 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

## Soft skills

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

See Schedules bachelor Astronomy

## Mode of instruction

Lectures and problem classes

## Assessment method

Written exam, see Examination schedules bachelor Astronomy

## Blackboard

Blackboard is not used for this course.

## Reading list

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

## Registration

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.

## Contact information

Lecturer: Prof.dr. P. (Paul) van der Werf

Assistants: Nastasha Wijers, Dong-Gang Wang

Course website: Astronomical Relativity

## Remarks

None