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 (jyoo physik.uzh.ch)
Teaching assistants:
Giovanni Piccoli (giovanni.piccoli 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
- Lecture 1: Introduction (slides)
II. Special Relativity (notes)
- Lecture 2: Lorentz transformation, length contraction, time dilation (notes)
- Lecture 3: Velocity/acceleration transformation, uniform acceleration, Twin paradox
- Lecture 4: Barn-Pole paradox, relativistic Doppler effect, relativistic beaming
- Lecture 5: Relativistic dynamics, Tensor manipulation, E&M
III. Going beyond Special Relativity (notes)
- Lecture 6: Equivalence Principle, General Covariance, Mach Principle
- Lecture 7: Geodesic equation, Christoffel symbols, Newtonian limit
IV. Tensor Algebra & Curved Spacetime (notes)
- Lecture 8: Manifold, Curved spacetime
- Lecture 9: Mathematica tutorial for symbolic operations
- Lecture 10: Lie derivative, covariant derivative, parallel transport, tensor density of weight
- Lecture 11: Levi-Civita symbols, metric geodesic (pdf), differential forms
- Lecture 12: non-commutativity of covariant derivatives, Riemann tensor, Weyl tensor
- Lecture 13: Killing vectors, symmetric spacetime, geodesic deviation equation
V. General Theory of Relativity (notes)
- Lecture 14: Derivation of the Einstein equation
- Lecture 15: Structure of the Field Equation, Cauchy Problem, Variational method
- Lecture 16: Einstein-Hilbert Action, Energy-Momentum Tensor, Palatini method
VI. Solar System Tests of General Relativity (notes)
- Lecture 17: Spherically symmetric, static solution, radial geodesic (timelike and null)
- Lecture 18: Newtonian and Relativistic Binet equation (pdf)
- Lecture 19: General motion around BH. Effective potential
- Lecture 20: Parametrized Post-Newtonian, Precession of Mercury perihelion, Light deflection, Time delay measurement
VII. Gravitational Waves
- Lecture 21: Waves in E&M vs Gravitation
- Lecture 22: Quadrupole moments of a black hole binary system, Coalescence time scale
- Lecture 23: Vacuum solution with the weak field approximation
- Lecture 24: Harmonic gauge, TT gauge, gravitational wave polarizations
- Lectures 25-26: Gravitational wave solutions to the Einstein equation
Exercise sheets: