"Special relativity"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5 (.*)">” 문자열을 “==” 문자열로) |
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| 11번째 줄: | 11번째 줄: | ||
| − | + | ==review of Maxwell's equation== | |
* [[Electromagnetics|Electromagnetism]]<br> | * [[Electromagnetics|Electromagnetism]]<br> | ||
| 19번째 줄: | 19번째 줄: | ||
| − | + | ==Lorentz transformation and Maxwell's equation== | |
* http://en.wikipedia.org/wiki/Lorentz_transformation<br> | * http://en.wikipedia.org/wiki/Lorentz_transformation<br> | ||
| 30번째 줄: | 30번째 줄: | ||
| − | + | ==Vacuum field equation and gravitational field equation== | |
* gravitational potentail satisfies the following equation (Poisson's equation)<br><math>\nabla^2 \phi = - 4 \pi G \rho</math><br> | * gravitational potentail satisfies the following equation (Poisson's equation)<br><math>\nabla^2 \phi = - 4 \pi G \rho</math><br> | ||
| 40번째 줄: | 40번째 줄: | ||
| − | + | ==energy-momentum tensor== | |
* also called as stress-energy tensor<br> | * also called as stress-energy tensor<br> | ||
| 53번째 줄: | 53번째 줄: | ||
| − | + | ==relativistic Vacuum field equation== | |
| 61번째 줄: | 61번째 줄: | ||
| − | + | ==relativistic matter field equation== | |
* [[Einstein field equation]]<br><math>R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}</math><br> | * [[Einstein field equation]]<br><math>R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}</math><br> | ||
| 69번째 줄: | 69번째 줄: | ||
| − | + | ==history== | |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 97번째 줄: | 97번째 줄: | ||
| − | + | ==related items== | |
* [http://pythagoras0.springnote.com/pages/1951508 미분기하학]<br> | * [http://pythagoras0.springnote.com/pages/1951508 미분기하학]<br> | ||
| 105번째 줄: | 105번째 줄: | ||
| − | + | ==encyclopedia== | |
* [http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation]<br> | * [http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation]<br> | ||
| 120번째 줄: | 120번째 줄: | ||
| − | + | ==books== | |
* http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12<br> | * http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12<br> | ||
| 134번째 줄: | 134번째 줄: | ||
| − | + | ==articles== | |
* [http://www.fourmilab.ch/etexts/einstein/specrel/www/ On the electrodynamics of moving bodies]<br> | * [http://www.fourmilab.ch/etexts/einstein/specrel/www/ On the electrodynamics of moving bodies]<br> | ||
| 150번째 줄: | 150번째 줄: | ||
| − | + | ==question and answers(Math Overflow)== | |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
| 159번째 줄: | 159번째 줄: | ||
| − | + | ==blogs and webpage== | |
* [http://www.zweigmedia.com/diff_geom/tc.html Introduction to Differential Geometry and General Relativity]<br> | * [http://www.zweigmedia.com/diff_geom/tc.html Introduction to Differential Geometry and General Relativity]<br> | ||
| 172번째 줄: | 172번째 줄: | ||
| − | + | ==links== | |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
2012년 10월 28일 (일) 16:49 판
four-vector
- can be transformed by Lorentz transformation
- examples
- space-time (ct,x,y,z)
- four momentum (m,mv_1,mv_2,mv_3)
- electromagnetic field
review of Maxwell's equation
Lorentz transformation and Maxwell's equation
- http://en.wikipedia.org/wiki/Lorentz_transformation
- one-dimensional example
\(E_{tt}-E_{zz}=0\)
Vacuum field equation and gravitational field equation
- gravitational potentail satisfies the following equation (Poisson's equation)
\(\nabla^2 \phi = - 4 \pi G \rho\) - \(\rho\) is the matter density
- in relativity theory, the metric plays the role of gravitational potential
energy-momentum tensor
- also called as stress-energy tensor
- describe the densities and flows of energy and momentum
- all forms of mass-energy can be sources of gravitational fields
- the stress-energy tensor \(T_{\mu \nu}\) acts as a source of the gravitational field
relativistic Vacuum field equation
relativistic matter field equation
- Einstein field equation
\(R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\)
history
하위페이지
encyclopedia
- http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
- http://en.wikipedia.org/wiki/Einstein_field_equations
- http://en.wikipedia.org/wiki/Solutions_of_the_Einstein_field_equations
-
http://en.wikipedia.org/wiki/Lorentz_covariant - [1]http://en.wikipedia.org/wiki/Four-vector
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12
- 2010년 books and articles
- http://gigapedia.info/1/relativity
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- On the electrodynamics of moving bodies
- A. Einstein, 1905
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[2]
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
question and answers(Math Overflow)
blogs and webpage
- Introduction to Differential Geometry and General Relativity
- Lecture Notes by Stefan Waner
- Lecture Notes by Stefan Waner