"Einstein field equation"의 두 판 사이의 차이

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==introduction==
  
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* prerequiste : Riemann tensor, the Ricci tensor, and the Ricci scalar
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*  relativistic matter field equation
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:<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
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* one can regard this as a partial differential equation for a metric
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==steps to solve an Einstein equation==
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*  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
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*  find the components of the curvature tensor
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*  find the components of the Einstein tensor
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==Einstein-Hilbert action==
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*  Einstein-Hilbert action
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:<math>S= - {1 \over 2\kappa}\int R \sqrt{-g} \, d^4x </math>
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:<math>\kappa = {8 \pi G \over c^4} </math>
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==equation of motion==
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* 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==
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*  Einstein
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*  eventually led to the graviton idea\
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==history==
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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==related items==
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* [[Einstein metrics and Ricci solitons]]
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* [[cosmological constant]]
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* [[differential geometry and topology]]
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* [[Yang-Mills Theory(Non-Abelian gauge theory)]]
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* [[string theory and Einstein equations]]
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==encyclopedia==
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* http://en.wikipedia.org/wiki/Einstein_field_equations
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* http://en.wikipedia.org/wiki/Riemann_curvature_tensor
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* http://en.wikipedia.org/wiki/Ricci_curvature
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* http://en.wikipedia.org/wiki/Scalar_curvature
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==expositions==
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* 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.
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* 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==
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* 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.
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* 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]]
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[[분류:math and physics]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q273711 Q273711]
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===Spacy 패턴 목록===
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* [{'LOWER': 'einstein'}, {'LOWER': 'field'}, {'LEMMA': 'equation'}]
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* [{'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



related items



encyclopedia


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

Spacy 패턴 목록

  • [{'LOWER': 'einstein'}, {'LOWER': 'field'}, {'LEMMA': 'equation'}]
  • [{'LOWER': 'einstein'}, {'LOWER': "'s"}, {'LEMMA': 'equation'}]
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