"Einstein field equation"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→메타데이터) |
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| (사용자 3명의 중간 판 23개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
| − | + | ==introduction== | |
* prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar | * prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar | ||
| − | * relativistic matter field equation | + | * relativistic matter 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> where <math>R_{\mu \nu}</math> is the Ricci curvature tensor, <math>R</math> the Ricci scalar curvature, <math>\Lambda</math> is the [[cosmological constant]], <math>T_{\mu \nu}</math> momentum-energy tensor | ||
| + | * one can regard this as a partial differential equation for a metric | ||
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| − | + | ==steps to solve an Einstein equation== | |
| − | + | * consider a metric, for example<math>ds^2=-dt^2+e^{2b(t,r)}dr^2+R(t,r)d\phi^2</math> where b, R are unknown functions | |
| + | * find the components of the curvature tensor | ||
| + | * find the components of the Einstein tensor | ||
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| − | + | ==Einstein-Hilbert action== | |
| − | + | * Einstein-Hilbert action | |
| + | :<math>S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x </math> | ||
| + | :<math>\kappa = {8 \pi G \over c^4} </math> | ||
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| − | + | ==equation of motion== | |
| − | * http://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action#Derivation_of_Einstein.27s_field_equations | + | * http://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action#Derivation_of_Einstein.27s_field_equations |
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| − | + | ==solutions example : Schwarzschild black hole== | |
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| − | + | ==solutions example : gravitational wave== | |
| − | * | + | * Einstein |
| − | + | * eventually led to the graviton idea\ | |
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| − | + | ==history== | |
| − | * | + | * http://www.google.com/search?hl=en&tbs=tl:1&q= |
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| − | + | ==related items== | |
| + | * [[Einstein metrics and Ricci solitons]] | ||
| + | * [[cosmological constant]] | ||
| + | * [[differential geometry and topology]] | ||
| + | * [[Yang-Mills Theory(Non-Abelian gauge theory)]] | ||
| + | * [[string theory and Einstein equations]] | ||
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| − | + | ==encyclopedia== | |
| − | + | * http://en.wikipedia.org/wiki/Einstein_field_equations | |
| − | + | * http://en.wikipedia.org/wiki/Riemann_curvature_tensor | |
| − | + | * http://en.wikipedia.org/wiki/Ricci_curvature | |
| − | + | * http://en.wikipedia.org/wiki/Scalar_curvature | |
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| − | + | ==expositions== | |
| + | * Weinstein, Galina. ‘Did Einstein “Nostrify” Hilbert’s Final Form of the Field Equations for General Relativity?’. arXiv:1412.1816 [physics], 4 December 2014. http://arxiv.org/abs/1412.1816. | ||
| + | * Boehmer, Christian G., and Nyein Chan. “Dynamical Systems in Cosmology.” arXiv:1409.5585 [gr-Qc], September 19, 2014. http://arxiv.org/abs/1409.5585. | ||
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| − | + | ==articles== | |
| + | * Curiel, Erik. “A Simple Proof of the Uniqueness of the Einstein Field Equation in All Dimensions.” arXiv:1601.03032 [gr-Qc, Physics:physics], January 12, 2016. http://arxiv.org/abs/1601.03032. | ||
| + | * De Freitas, Gabriel Bernardi, Mahdi Godazgar, and Harvey S. Reall. “Uniqueness of the Kerr-de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions.” arXiv:1501.02837 [gr-Qc, Physics:hep-Th], January 12, 2015. http://arxiv.org/abs/1501.02837. | ||
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| − | + | [[분류:physics]] | |
| + | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
| − | * [ | + | ==메타데이터== |
| − | * [ | + | ===위키데이터=== |
| − | * [ | + | * ID : [https://www.wikidata.org/wiki/Q273711 Q273711] |
| − | + | ===Spacy 패턴 목록=== | |
| + | * [{'LOWER': 'einstein'}, {'LOWER': 'field'}, {'LEMMA': 'equation'}] | ||
| + | * [{'LOWER': 'einstein'}, {'LOWER': "'s"}, {'LEMMA': 'equation'}] | ||
2021년 2월 17일 (수) 02:09 기준 최신판
introduction
- prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar
- relativistic matter field equation
\[R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}\] where \(R_{\mu \nu}\) is the Ricci curvature tensor, \(R\) the Ricci scalar curvature, \(\Lambda\) is the cosmological constant, \(T_{\mu \nu}\) momentum-energy tensor
- one can regard this as a partial differential equation for a metric
steps to solve an Einstein equation
- consider a metric, for example\(ds^2=-dt^2+e^{2b(t,r)}dr^2+R(t,r)d\phi^2\) where b, R are unknown functions
- find the components of the curvature tensor
- find the components of the Einstein tensor
Einstein-Hilbert action
- Einstein-Hilbert action
\[S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x \] \[\kappa = {8 \pi G \over c^4} \]
equation of motion
solutions example : Schwarzschild black hole
solutions example : gravitational wave
- Einstein
- eventually led to the graviton idea\
history
- Einstein metrics and Ricci solitons
- cosmological constant
- differential geometry and topology
- Yang-Mills Theory(Non-Abelian gauge theory)
- string theory and Einstein equations
encyclopedia
- http://en.wikipedia.org/wiki/Einstein_field_equations
- http://en.wikipedia.org/wiki/Riemann_curvature_tensor
- http://en.wikipedia.org/wiki/Ricci_curvature
- http://en.wikipedia.org/wiki/Scalar_curvature
expositions
- Weinstein, Galina. ‘Did Einstein “Nostrify” Hilbert’s Final Form of the Field Equations for General Relativity?’. arXiv:1412.1816 [physics], 4 December 2014. http://arxiv.org/abs/1412.1816.
- Boehmer, Christian G., and Nyein Chan. “Dynamical Systems in Cosmology.” arXiv:1409.5585 [gr-Qc], September 19, 2014. http://arxiv.org/abs/1409.5585.
articles
- Curiel, Erik. “A Simple Proof of the Uniqueness of the Einstein Field Equation in All Dimensions.” arXiv:1601.03032 [gr-Qc, Physics:physics], January 12, 2016. http://arxiv.org/abs/1601.03032.
- De Freitas, Gabriel Bernardi, Mahdi Godazgar, and Harvey S. Reall. “Uniqueness of the Kerr-de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions.” arXiv:1501.02837 [gr-Qc, Physics:hep-Th], January 12, 2015. http://arxiv.org/abs/1501.02837.
메타데이터
위키데이터
- ID : Q273711
Spacy 패턴 목록
- [{'LOWER': 'einstein'}, {'LOWER': 'field'}, {'LEMMA': 'equation'}]
- [{'LOWER': 'einstein'}, {'LOWER': "'s"}, {'LEMMA': 'equation'}]