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.
Lectures by:
Prof. Dr. Jaiyul Yoo (jaiyul.yoo@uzh.ch)
Teaching assistants:
Dr. Francesca Lepori (francesca.lepori2@uzh.ch) and Christopher Magnoli (christopher.magnoli@uzh.ch)
Prerequisites:
Basic knowledge of special relativity and classical mechanastro 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.
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 Astrophysastro, 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 Physastro, 1991, Freeman
- Anthony Zee, Einstein Gravity in a Nutshell, 2013, Princeton University
Lectures: pdf
I. Introduction and Historical Developments
- Lecture 1: Introduction (slides)
II. Special Relativity (notes)
- Lecture 2: Lorentz transformation, length contraction, time dilation
- Lecture 3: Paradoxes in special relativity, velocity/acceleration transformation
- Lecture 4: uniform acceleration, relativistic Doppler effect, relativistic beaming
III. Going beyond Special Relativity (notes)
- Lecture 5: Equivalence Principle, Geodesic Equation, Christoffel symbols
- Lecture 6: General Covariance, Mach Principle
IV. Tensor Algebra & Curved Spacetime (notes)
- Lecture 7: Manifold, Curved spacetime
- Lecture 8: Lie derivative, covariant derivative, parallel transport, tensor density of weight
- Lecture 9: Levi-Civita symbols, metric geodesic, definition of Riemann tensor
- Lecture 10: non-commutativity of covariant derivatives, Riemann tensor, Weyl tensor
- Lecture 11: Killing vectors, symmetric spacetime, tidal tensor
- Lecture 12: Geodesic deviation equation, Palatini identity, Riemann normal coordinate
V. General Theory of Relativity (notes)
- Lecture 13: Derivation of the Einstein field equation
- Lecture 14: Variational Method, Einstein-Hilbert action
- Lecture 15: Structure of the field equation, Cauchy problem, Palatini method
VI. Solar System Tests of General Relativity (notes)
- Lecture 16: Spherically symmetric, static solution, radial geodesic (timelike and null)
- Lecture 17: Newtonian dynamics, Binet equation
- Lecture 18: General motion around BH. Effective potential (plot)
- Lecture 19: Parametrized Post-Newtonian, Precession of Mercury perihelion, light deflection
VII. Gravitational Waves (notes)
- Lecture 20: Waves in E&M vs Gravitation
- Lecture 21: Quadrupole moments of a black hole binary system, Chirp mass
- Lecture 22: Linearized Einstein equation, Harmonic gauge condition, Wave equation
- Lecture 23: Gravitational wave solutions to the Einstein equation
- Lecture 24: Quadrupolar formula from a binary black hole
- Lecture 25: Gravitational Wave Experiments: LIGO, LISA, PTA
- Lecture 26: Summary
Exercise sheets: