# Astronomical Relativity

Course
2022-2023

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

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 sucessfully 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 the 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, see Examination schedules bachelor Astronomy

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

## Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.

## Contact

Lecturer: Dr. E.M. (Elena) Rossi
Assistants: Nicolo Veronesi, Anna Balaudo, Brigitte Pruijt, Michel Kaverman, Floris Fassin

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