# Astronomical Relativity

Course
2024-2025

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

Schedule

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have successfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go to the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## Mode of instruction

Lectures and problem classes

## Assessment method

Written exam

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

## Registration

As a student, you are responsible for registering on time, i.e. 14 days before the start of the course. This can be done via Mystudymap. You do this twice a year: once for the courses you want to take in semester 1 and once for the courses you want to take in semester 2. Please note: late registration is not possible.

Registration for courses in the first semester is possible from July; registration for courses in the second semester is possible from December. First-year bachelor students are registered for semester 1 by the faculty student administration; they do not have to do this themselves. For more information, see this page

In addition, it is mandatory for all students, including first-year bachelor students, to register for exams. This can be done up to and including 10 calendar days prior to the exam or up to five calendar days in case of a retake exam. You cannot participate in the exam or retake without a valid registration in My Studymap.

Extensive FAQ's on MyStudymap can be found here.

## Contact

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

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