課程資訊
課程名稱
 廣義相對論
General Relativity 
開課學期
 104-2 
授課對象
 理學院  天文物理研究所  
授課教師
 陳義裕 
課號
 AsPhys8017 
課程識別碼
 244 D1120 
班次
  
學分
 3 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期一2,3,4(9:10~12:10) 
上課地點
 新物111 
備註
 1.天文必選 2.在新物111上課
總人數上限：50人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1042AsPhys8017_ 
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課程概述

This course discusses the elements of the classical general theory of relativity. It is expected that the students taking this course are already familiar with the language of the special theory of relativity, classical mechanics, and classical electromagnetism.

The mathematical prerequisites include linear algebra, differential and integral
calculus, vector calculus, and partial differential equations. In addition, do anticipate some messy calculations along the way. 

課程目標
 Outline of Contents:
(An * means it will be covered only when time permits.)

1. Lorentz transformation of special relativity:
 Lorentz transformation without light
 Clocks go out of sync when in motion
 Some simple “paradoxes”
 Spacetime diagram and 4-vectors
 Geometrization of the law of conservation of energy-momentum
 Symmetry can be a severe constraint put in by hand
 Conservation law is a local thing
 Coordinate basis and the metric

2. Uniformly accelerated observer, and his neighbors:
 Uniform acceleration is meaningful only to oneself
 Neighbors keeping a fixed distance upstairs is not experiencing the same acceleration
 An event horizon somewhere downstairs and particle trajectories
 Nothing strange happens when falling into the event horizon
 The equivalence principle
 Curving of the time axis induces gravity
 The gravitational redshift
 The twin paradox

3. The Schwarzschild solution:
 A freely falling test particle moves on a “geodesic”
 The Schwarzschild metric
 Embedding of the spatial geometry
 Extra attraction caused by curved space
 Bending of starlight near the sun, and why Einstein got it wrong the first time around
 Gravitational lensing
 Why GR causes the precession of planetary orbits about the sun
 The event horizon
 Nothing strange happens when falling into the event horizon
 Black holes
 Some interesting orbits around a black hole
 Possibility of wormholes and time machines

4. Curvature and tensors:
 Curvature of a spatial curve
 Curvature of a curve lying on a surface
 Curvature of a surface
 Detecting the curvature without leaving the surface
 Concept of “connection” and covariant derivative of a vector field
 Parallel transport
 Thomas precession as a manifestation of parallel transport
 Geodetic effect in the Schwarzschild metric
 An aside on dual space, tensors, and all that
 Strain tensor, stress tensor, and stress-energy tensor
 A freely falling particle moves on a geodesic to conserve energy
 The Riemann curvature tensor
 Geodesic deviation

5. Einstein's field equation:
 From Newton's law of gravitation to its relativistic generalization
 The Schwarzschild solution derived

6. The weak field approximation*:
 The weak field approximation and interpretation
 Gravitational waves

7. Cosmology*:
 The Friedman-Robertson-Walker metric
 The expanding universe
 
課程要求
 Grading Policy:
In contrast to most other courses, this one is graded on a Pass/Fail basis.
Homework: 40%
One Major Exam: 60%
You pass the course with a total score of no less than 60%. 
預期每週課後學習時數
  
Office Hours
  
指定閱讀
Textbook: None, officially. 
參考書目
 Some easily accessible readings:
1. J. Foster and J.D. Nightingale, A Short Course in General Relativity, 3rd ed,
Springer
(2006). NTU campus access:
http://rd.springer.com/book/10.1007%2F978-0-387-27583-3
2. N. M. J. Woodhouse, General Relativity, Springer (2007). NTU campus access:
http://rd.springer.com/book/10.1007%2F978-1-84628-487-8
3. Benjamin Crowell, General Relativity (2009). Free online access:
http://www.lightandmatter.com/genrel/
4. Sean M. Carroll, Lecture Notes on General Relativity (1997). Free online access:
http://arxiv.org/abs/gr‐qc/9712019 
評量方式
(僅供參考)
    
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