Introduction to General Relativity
General relativity is one of the most revolutionary theories in 20th‑century physics. It fundamentally changed our understanding of space, time, and gravity. This course provides a systematic introduction to general relativity for students with a background in physics / mathematics.
Starting from the historical development of gravitational theory, we will examine the deep tension between Newtonian gravity and special relativity, and introduce the equivalence principle as the key physical insight. The course then systematically develops the mathematical tools required to describe curved spacetime – tensor analysis and Riemannian geometry. On this foundation, we derive Einstein’s field equations and study their applications in spherically symmetric spacetimes (the Schwarzschild solution), the weak‑field limit (Newtonian limit and classical tests), black hole physics, and elementary cosmology.
The course emphasises the interplay between physical intuition and mathematical structure, aiming to build a solid foundation for further studies in astrophysics, cosmology, and gravitational‑wave physics.
Starting from the historical development of gravitational theory, we will examine the deep tension between Newtonian gravity and special relativity, and introduce the equivalence principle as the key physical insight. The course then systematically develops the mathematical tools required to describe curved spacetime – tensor analysis and Riemannian geometry. On this foundation, we derive Einstein’s field equations and study their applications in spherically symmetric spacetimes (the Schwarzschild solution), the weak‑field limit (Newtonian limit and classical tests), black hole physics, and elementary cosmology.
The course emphasises the interplay between physical intuition and mathematical structure, aiming to build a solid foundation for further studies in astrophysics, cosmology, and gravitational‑wave physics.
Lecturer
Date
13th October ~ 31st December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 16:10 - 17:50 | A14-203 | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
Classical mechanics (Newtonian and Lagrangian mechanics); Electrodynamics (Maxwell’s equations); Special relativity (Lorentz transformations, Minkowski spacetime) Linear algebra and multivariable calculus (partial differential equations, vector calculus)
Syllabus
The following is a 16‑week plan (3 hours per week). Subject to change.
Week Topic Main Contents
1 Introduction and Physical Preliminaries Newtonian gravity and its difficulties; review of special relativity (Lorentz transformations, Minkowski spacetime, four‑vector notation)
2 Equivalence Principle and Geometrisation Formulations and experimental tests of the equivalence principle; weak vs. strong equivalence principle; gravity as spacetime curvature
3 Tensor Algebra (I) Manifolds and coordinate transformations; covariant and contravariant tensors; algebraic operations
4 Tensor Algebra (II) The metric tensor; Minkowski vs. Riemannian metrics; contraction and raising/lowering indices
5 Tensor Analysis (I) Covariant derivative and Christoffel symbols; geodesic equation
6 Tensor Analysis (II) Parallel transport; Riemann curvature tensor and its algebraic properties; Bianchi identities
7 Einstein’s Field Equations (I) Geometrisation of Newton’s field equation; structure and derivation of Einstein’s field equations
8 Einstein’s Field Equations (II) Einstein‑Hilbert action; energy‑momentum tensor; cosmological constant
9 Schwarzschild Solution and Black Holes (I) Spherically symmetric metrics; derivation of the Schwarzschild solution
10 Schwarzschild Solution and Black Holes (II) Geometry of Schwarzschild black holes; event horizon; singularity; Kruskal coordinates
11 Classical Tests of General Relativity Light deflection; Mercury’s perihelion advance; radar echo delay
12 Weak‑Field Limit and Gravitational Waves Linearised Einstein equations; generation and propagation of gravitational waves; detection
13 Elementary Cosmology (I) Cosmological principle; FLRW metric
14 Elementary Cosmology (II) Friedmann equations; simple cosmological models (matter‑dominated, radiation‑dominated, cosmological constant)
15 Selected Advanced Topics Kerr black holes, black hole thermodynamics, gravitational‑wave astronomy, black‑hole imaging (choose according to progress)
16 Review and Summary Overall framework; typical problem solving; Q&A session
Week Topic Main Contents
1 Introduction and Physical Preliminaries Newtonian gravity and its difficulties; review of special relativity (Lorentz transformations, Minkowski spacetime, four‑vector notation)
2 Equivalence Principle and Geometrisation Formulations and experimental tests of the equivalence principle; weak vs. strong equivalence principle; gravity as spacetime curvature
3 Tensor Algebra (I) Manifolds and coordinate transformations; covariant and contravariant tensors; algebraic operations
4 Tensor Algebra (II) The metric tensor; Minkowski vs. Riemannian metrics; contraction and raising/lowering indices
5 Tensor Analysis (I) Covariant derivative and Christoffel symbols; geodesic equation
6 Tensor Analysis (II) Parallel transport; Riemann curvature tensor and its algebraic properties; Bianchi identities
7 Einstein’s Field Equations (I) Geometrisation of Newton’s field equation; structure and derivation of Einstein’s field equations
8 Einstein’s Field Equations (II) Einstein‑Hilbert action; energy‑momentum tensor; cosmological constant
9 Schwarzschild Solution and Black Holes (I) Spherically symmetric metrics; derivation of the Schwarzschild solution
10 Schwarzschild Solution and Black Holes (II) Geometry of Schwarzschild black holes; event horizon; singularity; Kruskal coordinates
11 Classical Tests of General Relativity Light deflection; Mercury’s perihelion advance; radar echo delay
12 Weak‑Field Limit and Gravitational Waves Linearised Einstein equations; generation and propagation of gravitational waves; detection
13 Elementary Cosmology (I) Cosmological principle; FLRW metric
14 Elementary Cosmology (II) Friedmann equations; simple cosmological models (matter‑dominated, radiation‑dominated, cosmological constant)
15 Selected Advanced Topics Kerr black holes, black hole thermodynamics, gravitational‑wave astronomy, black‑hole imaging (choose according to progress)
16 Review and Summary Overall framework; typical problem solving; Q&A session
Reference
R. Wald, General Relativity, University of Chicago Press
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
I am an Associate Professor at BIMSA. I joined BIMSA in the summer of 2025. My Research area is statistical genetics, where I develop statistical and computational methods, mainly from Bayesian perspective, with targeted applications in genomic studies and genetic diagnosis. Currently I am working on studying haplotype variation using deep learning models. I am also interested in studying genetic determinants of autism, and early cancer screening.