Introduction to general relativity

GEOPlanet, Warsaw4PHD graduate schools

Winter semester 2023/2024

ECTS credits: 3

Course time: Tuesday 9.00-11.00, via Zoom


Lecturer: Mikołaj Korzyński (Center for Theoretical Physics, PAS)

Warsaw University of Technology (Politechnika Warszawska)  
Faculty of Electronics and Information Technology  
(Wydział Elektroniki i Technik Informacyjnych)  
ul. Nowowiejska 15/19  
00-665 Warszawa  
Room 459

Lecture notes and recordings

Lecture recordings: YouTube channel

Problem sheets

Please send the solutions via email to I prefer PDF's (for example LaTeX-generated) or common graphic formats (for example scans of your hand-written notes).

  1. Problem sheet 1

  2. Problem sheet 2

  3. Problem sheet 3

  4. Problem sheet 4

  5. Problem sheet 5

General information

  1. Course type: This is an introductory course of general relativity with emphasis on astrophysical and cosmological applications

  2. Intended for: graduate students of theoretical physics, astrophysics, astronomy etc.
    Why should you take this course?

  3. Prerequisites:

  4. Organization:

  5. Textbooks:
    There will be no official course textbook, but I can recommend the following books as additional reading:

  6. Course webpage with notes & problem sheets:

My plan for the incoming lectures


This is a rather ambitious outline, we may not be able to cover all of the material from the last few topics.

  1. Introduction:
  2. Special vs general relativity:
  3. Mathematical language = differential geometry:
  4. Einstein equations: how matter curves spacetime
  5. Newtonian approximation
  6. Linearized gravity
  7. Exact solutions: Schwarzschild metric
  8. Exact solutions: Kerr metric
  9. Exact solutions: FLRW metric
  10. Gravitational lensing
  11. Tests of GR, classical and new
  12. Perhaps: 3+1 splitting, ADM formalism