"Special relativity"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “4909919” 문자열을 “” 문자열로) |
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| − | ==four- | + | ==four-vector == |
* can be transformed by Lorentz transformation | * can be transformed by Lorentz transformation | ||
| − | * examples | + | * examples |
| − | ** space-time (ct,x,y,z) | + | ** space-time $(ct,x,y,z)$ |
| − | ** four momentum (m,mv_1,mv_2,mv_3) | + | ** four momentum $(m,mv_1,mv_2,mv_3)$ |
** electromagnetic field | ** electromagnetic field | ||
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==review of Maxwell's equation== | ==review of Maxwell's equation== | ||
| − | * [[Electromagnetics|Electromagnetism]] | + | * [[Electromagnetics|Electromagnetism]] |
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==Lorentz transformation and Maxwell's equation== | ==Lorentz transformation and Maxwell's equation== | ||
| − | * http://en.wikipedia.org/wiki/Lorentz_transformation | + | * http://en.wikipedia.org/wiki/Lorentz_transformation |
| − | * | + | * one-dimensional example |
| + | :<math>E_{tt}-E_{zz}=0</math> | ||
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| − | + | ==Vacuum field equation and gravitational field equation== | |
| − | + | * gravitational potentail satisfies the following equation (Poisson's equation) | |
| + | :<math>\nabla^2 \phi = - 4 \pi G \rho</math> | ||
| + | * <math>\rho</math> is the matter density | ||
| + | * in relativity theory, the metric plays the role of gravitational potential | ||
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==energy-momentum tensor== | ==energy-momentum tensor== | ||
| − | * also called as stress-energy tensor | + | * also called as stress-energy tensor |
| − | * describe the densities and flows of energy and momentum | + | * describe the densities and flows of energy and momentum |
| − | * all forms of mass-energy can be sources of gravitational fields | + | * all forms of mass-energy can be sources of gravitational fields |
| − | * the stress-energy tensor <math>T_{\mu \nu}</math> acts as a source of the gravitational field | + | * the stress-energy tensor <math>T_{\mu \nu}</math> acts as a source of the gravitational field |
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==relativistic Vacuum field equation== | ==relativistic Vacuum field equation== | ||
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| − | ==relativistic | + | ==relativistic matter field equation== |
| − | * [[Einstein field equation]] | + | * [[Einstein field equation]] |
| + | :<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> | ||
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| − | + | ==related items== | |
| − | + | * {{수학노트|url=미분기하학}} | |
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| − | + | === 하위페이지 === | |
| − | + | * [[special and general relativity]] | |
| + | ** [[cosmological constant]] | ||
| + | ** [[Einstein field equation]] | ||
| + | ** [[energy-momentum tensor]] | ||
| + | ** [[Hamiltonian formulation of GR]] | ||
| + | ** [[light cone coordinates and gauge]] | ||
| + | ** [[relativistic point particle]] | ||
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==encyclopedia== | ==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/Einstein_field_equations |
| − | * http://en.wikipedia.org/wiki/Solutions_of_the_Einstein_field_equations | + | * http://en.wikipedia.org/wiki/Solutions_of_the_Einstein_field_equations |
| − | * | + | * http://en.wikipedia.org/wiki/Lorentz_covariant |
| − | * | + | * http://en.wikipedia.org/wiki/Four-vector |
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==books== | ==books== | ||
| − | * http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12 | + | * http://gigapedia.com/items/45025/relativity-demystified---a-self-teaching-guide--2005-12 |
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==articles== | ==articles== | ||
| − | * [http://www.fourmilab.ch/etexts/einstein/specrel/www/ On the electrodynamics of moving bodies] | + | * [http://www.fourmilab.ch/etexts/einstein/specrel/www/ On the electrodynamics of moving bodies] |
** A. Einstein, 1905 | ** A. Einstein, 1905 | ||
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==blogs and webpage== | ==blogs and webpage== | ||
| − | * [http://www.zweigmedia.com/diff_geom/tc.html Introduction to Differential Geometry and General Relativity] | + | * [http://www.zweigmedia.com/diff_geom/tc.html Introduction to Differential Geometry and General Relativity] |
| − | ** Lecture Notes by Stefan Waner | + | ** Lecture Notes by Stefan Waner |
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:physics]] | [[분류:physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2014년 1월 5일 (일) 02:03 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
\[R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\]
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
- http://en.wikipedia.org/wiki/Four-vector
books
articles
- On the electrodynamics of moving bodies
- A. Einstein, 1905
blogs and webpage
- Introduction to Differential Geometry and General Relativity
- Lecture Notes by Stefan Waner