General Relativity & Astrophysics
Fall 2026, Peking University
$$R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8\pi G}{c^4} T_{\mu\nu}$$ “Matter tells spacetime how to curve, and spacetime tells matter how to move.”
This course is designed to be elementary, suitable for those who want a first grasp of the tremendous beauty of Einstein’s general relativity. I will try to keep the mathematics minimum (e.g. the differential geometry), and the physics clearly stated (e.g. the equivalence principle). In this class, students are supposed to learn,
- the logic behind Einstein’s general relativity,
- the ability to derive basic equations,
- fine interpretation of various phenomena in the relativistic astrophysics,
- the limitation of the class,
- as well as the direction to explore if one wants to master more advanced materials.
Though the class targets graduates who work on astrophysics or theoretical physics, it is in general eligible for graduate students (as well as the advanced undergraduates) with Science & Engineering background.
General Information
| When | 周二10-11节 |
| Where | |
| Prerequisite | Mathematics, Theoretical Mechanics, Electrodynamics |
| Textbook | 俞允强，《广义相对论引论(第二版)》（1997） |
| Reference | Bernard Schutz, A First Course in General Relativity (2009) |
| Matthias Blau, Lecture Notes on General Relativity [link] | |
| 陈斌，《广义相对论》（2018） | |
| Lecturer | Lijing Shao (邵立晶)；Office KIAA-217；lshao@pku.edu.cn |
| 【答疑时间】每周日14:00-15:00PM（建议来前联系，以免空跑） | |
| Teaching Assistant | |
| 网盘链接 | 猛戳这里 （倘若打开有误，请尝试重新刷新） |
Contents
| Content | Note |
| 0. 课程介绍 | |
| 1. 牛顿、麦克斯韦、爱因斯坦 | |
| 2. 狭义相对论 | HW1 (ddl: ) |
| 3. 黎曼几何简介 | HW2 (ddl: ) |
| 4. Einstein 场方程 | |
| 5. 真空球对称解 | HW3 (ddl: ) |
| 6. 弱场近似与实验检验 | HW4 (ddl: ) |
| 7. 中子星与黑洞 | HW5 (ddl: ) |
| 8. 引力波简介 | |
| 9. 宇宙学简介* | |
| 期末答疑 | |
| 期末考试（开卷） |