General Relativity

Sponsored by


Dr Volker Schlue, University of Melbourne


This course is an introduction to general relativity theory suitable for Honours/ Master’s students with a background in mathematics and physics alike. We motivate this theory of gravitation by drawing on ideas from Newton’s theory, special relativity, and electromagnetism. The course introduces students to elements of differential geometry, in particular geodesics, notions of curvature, and discusses the role of partial differential equations in the theory.

Following a discussion of the action principle, and the Einstein equations in the presence of matter, the course explores some of the main consequences of general relativity: The existence of gravitational waves, and the formation of black holes in gravitational collapse.

Course overview

Week 1: Special relativity, Newtonian gravity, and the equivalence principle

Week 2: Einstein’s field equations, conservation laws and the action principle

Week 3: General relativity as an evolution problem, and gravitational waves

Week 4: Black holes and gravitational collapse in spherical symmetry


This course is aimed at students in physics and mathematics at the MSc level. It is foundational in the sense that it is a “first course in general relativity”, and assumes only exposure to topics that are typically covered in undergraduate courses in physics (such as electromagnetism) or mathematics (such as differential equations, and geometry of surfaces). All concepts in differential geometry are motivated and introduced in the course.


  • Three assignments (submission of written solutions to problem sheets, 25% each)
  • oral exam (discussion of course content, 30 minutes, via zoom, 25%)

(may be subject to change)

Attendance requirements

Participation in all lectures and tutorials is expected.

For those completing the subject for their own knowledge/interest, evidence of at least 80% attendance at lectures and tutorials is required to receive a certificate of attendance.


This subject is based on the lecture notes General Relativity, by Volker Schlue, which are available online:
A revised and updated version will be provided during the summer school.

Not sure if you should sign up for this course?

Take this QUIZ to self-evaluate and get a measure of the key foundational knowledge required.

Dr Volker Schlue, University of Melbourne

Volker Schlue is a Lecturer in Pure Mathematics at the School of Mathematics and Statistics at the University of Melbourne. He obtained his PhD from the University of Cambridge, under the supervision of Mihalis Dafermos, and held postdoctoral fellowships at the University of Toronto, and at MSRI, in Berkeley, where he was mentored by Spyros Alexakis, and Hans Lindblad. He also held a postdoctoral position at Sorbonne University, in Paris, where he was supervised by Jeremie Szeftel, before arriving in Melbourne in 2018. His research interests are in hyperbolic partial differential equations, differential geometry, geometric analysis, and in particular mathematical general relativity.