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課程名稱 |
廣義相對論
General Relativity |
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開課學期 |
105-2 |
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授課對象 |
理學院 物理學研究所 |
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授課教師 |
王名儒 |
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課號 |
AsPhys8017 |
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課程識別碼 |
244 D1120 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一2,3,4(9:10~12:10) |
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上課地點 |
新物111 |
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備註 |
1.天文必選
2.在新物111上課
總人數上限：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052AsPhys8017_1 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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. |
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課程目標 |
Outline of Contents:
1. Lorentz transformation of special relativity:
Time dilation and Space contraction
Some simple “paradoxes”
Spacetime diagram and 4-vectors
Relativistic particle mechanics
Electromagnetism in vacuum
2. Uniformly accelerated observer:
The equivalence principle
The gravitational redshift
The twin paradox
3. 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
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
4. Einstein's field equation:
From Newton's law of gravitation to its relativistic generalization
The Schwarzschild solution derived
5. 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
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
6. The weak field approximation:
The weak field approximation and interpretation
Gravitational waves
7. Cosmology:
The Cosmological spacetimes
The FRW universes
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課程要求 |
Grading Policy:
In contrast to most other courses, this one is graded on a Pass/Fail basis.
Homework and Class participation: 50%
One Major Exam: 50%
Some extra credits can be obtained by delivering term papers.
You need a final score above 60 in order to pass. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Relativity - Special, General, and Cosmological 2nd Ed.
Wolfgang Rindler
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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 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
class participation&home work |
50% |
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2. |
examination |
50% |
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