Astronomical Relativity
Collegejaar:  20182019 

Studiegidsnummer:  4072ASTRE 
Docent(en): 

Voertaal:  Engels 
Blackboard:  Nee 
EC:  6 
Niveau:  300 
Periode:  Semester 1 
 Wel Keuzevak
 Wel Contractonderwijs
 Wel Exchange
 Wel Study Abroad
 Geen Avondonderwijs
 Wel AlaCarte en Aanschuifonderwijs
 Geen Honours Class
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
 4vectors
 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 RobertsonWalker 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 nonrotating 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 behaviouroriented skills:
 Abstract thinking
 Correctly explaining and analyzing complex and nonintuitive 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 Einsteinâ€™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, DongGang Wang
Course website: Astronomical Relativity
Remarks
None
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