Class description: syllabus
In this course we study the theory of gravitation or general relativity.
We first review special relativity and its implications. Then we discuss
the equivalence principle and follow Einstein's path to develop general theory
of relativity. In the course, we also study mathematical concept and
tools necessary in curved spacetime. We discuss several tests of general
relativity, and time permitting we study applications of general relativity.
The course and exercise classes will be presented in English.
The lectures will be held separately from ETH this year. A different class under the same name will be taught by a different lecturer at ETH.
Lectures by:
Prof. Dr. Jaiyul Yoo (jyoo physik.uzh.ch)
Teaching assistants:
Lara Bohnenblust (lara.bohnenblust uzh.ch) and Matteo Magi (matteo.magi uzh.ch)
Prerequisites:
Basic knowledge of special relativity and classical mechanics is required
About the course:
The lectures will largely follow my own notes from many textbooks
and online material, which are mostly from D'Inverno, Hartle, Schutz, Weinberg,
and previous lectures
(note) from Prof. Jetzer.
My notes will be available online. Basic guideline (pdf) is as follows.
- Introduction and historical developments
- Special relativity
- Going beyond special relativity
- Tensor algebra and curved spacetime
- General theory of relativity
- Solar system test of general relativity
- Applications of general relativity
History of Einstein's path:
A concise description of Albert Einstein's path is given by the University
(pdf) in celebration of the return
of his PhD certificate to the University in 2022 (news, certificate). A more detailed description is available at ETH (Einstein).
Reference books:
(alphabetical order)
- Matthias Blau, Lecture Notes on General Relativity (website)
- Sean Carroll, Spacetime and Geometry, 2003, Pearson
- Sean Carroll, Lecture Notes on General Relativity (pdf), 1997
- Ray D'Inverno, Introducing Einstein's Relativity, 1992, Oxford University
- James Hartle, An Introduction to Einstein's General Relativity, 2002, Addison Wesley
- Philippe Jetzer, Lecture Notes on General Relativity (website)
- Misner, Thorne, Wheeler, Gravitation, 1973, Freeman
- Bernard Schutz, A First Course in General Relativity, 1985, Cambridge University
- Nobert Straumann, General Relativity with Applications to Astrophysics, 2004, Springer
- Robert Wald, General Relativity, 1984, Cambrdige University
- Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, 1972, John Wiley & Sons
- Taylor, Wheeler, Spacetime Physics, 1991, Freeman
- Anthony Zee, Einstein Gravity in a Nutshell, 2013, Princeton University
Lectures:
(pdf)
I. Introduction and Historical Developments
II. Special Relativity
- Lecture 2: Lorentz transformation, length contraction, time dilation, velocity transformation (notes)
- Lectures 3-5: Relativistic Doppler effects, acceleration, Rindler coordinates, paradoxes in special relativity, relativistic dynamics, E&M
III. Going beyond Special Relativity
- Lectures 6: Equivalence principle (notes), principle of general covariance, Christoffel symbols
- Lectures 7: Mathematica tutorial for symbolic manipulation
- Lectures 8: Mach's principle, geodesic motion in a gravitational field, Newtonian limit
IV. Tensor Algebra & Curved Spacetime
- Lectures 9-10: Lie derivative, covariant derivative, parallel transport, tensor density of weight, Levi-Civita symbol (pdf)
- Lectures 11-12: Riemann tensor, metric geodesic, non-commutativity of covariant derivatives, conformal tensor, Killing vector (notes)
- Lectures 13-14: Differential forms, Geodesic deviation equation, Riemann normal coordinate
V. General Theory of Relativity
- Lectures 15-16: Derivation of the Einstein equation, Structure of the equation, Variational method (pdf)
- Lecture 17: Einstein-Hilbert action, Palatini method, Cauchy problem
VI. Solar System Tests of General Relativity
- Lecture 18: Static, spherically symmetric solution
- Lectures 19-20: Radial geodesics, general motion, relativistic Binet equation in Schwarzschild metric (notes)
Lectures 21-22: Parametrized Post-Newtonian, Precession of Mercury perihelion, Light deflection, Time delay measurement
VII. Gravitational Waves
- Lectures 23-24: Waves in E&M vs Gravitation, Weak field, gravitational wave equation
- Lectures 25-26: TT gauge, gravitational wave solution
Exercise sheets: