## 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

## Transferable 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 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.

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

Assistants: Nicolo Veronesi, Raphael van Laak, Ernst Traanberg