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- Tetradic_Palatini_action abstract "The Einstein–Hilbert action for general relativity was first formulated purely in terms of the space-time metric. To take the metric and affine connection as independent variables in the action principle was first considered by Palatini. It is called a first order formulation as the variables to vary over involve only up to first derivatives in the action and so doesn't over complicate the Euler–Lagrange equations with terms coming from higher derivative terms. The tetradic Palatini action is another first-order formulation of the Einstein–Hilbert action in terms of a different pair of independent variables, known as frame fields and the spin connection. The use of frame fields and spin connections are essential in the formulation of a generally covariant fermionic action (see the article spin connection for more discussion of this) which couples fermions to gravity when added to the tetradic Palatini action.Not only is this needed to couple fermions to gravity and makes the tetradic action somehow more fundamental to the metric version, the Palatini action is also a stepping stone to more interesting actions like the self-dual Palatini action which can be seen as the Lagrangian basis for Ashtekar's formulation of canonical gravity (see Ashtekar's variables) or the Holst action which is the basis of the real variables version of Ashtekar's theory. Another important action is the Plebanski action (see the entry on the Barrett–Crane model), and proving that it gives general relativity under certain conditions involves showing it reduces to the Palatini action under these conditions.Here we present definitions and calculate Einstein's equations from the Palatini action in detail. These calculations can be easily modified for the self-dual Palatini action and the Holst action.".
- Tetradic_Palatini_action wikiPageID "39317081".
- Tetradic_Palatini_action wikiPageLength "19378".
- Tetradic_Palatini_action wikiPageOutDegree "21".
- Tetradic_Palatini_action wikiPageRevisionID "654519514".
- Tetradic_Palatini_action wikiPageWikiLink Affine_connection.
- Tetradic_Palatini_action wikiPageWikiLink Ashtekar_variables.
- Tetradic_Palatini_action wikiPageWikiLink Attilio_Palatini.
- Tetradic_Palatini_action wikiPageWikiLink Barrett–Crane_model.
- Tetradic_Palatini_action wikiPageWikiLink Category:General_relativity.
- Tetradic_Palatini_action wikiPageWikiLink Einstein_field_equations.
- Tetradic_Palatini_action wikiPageWikiLink Einstein_tensor.
- Tetradic_Palatini_action wikiPageWikiLink Einstein–Hilbert_action.
- Tetradic_Palatini_action wikiPageWikiLink Euler–Lagrange_equation.
- Tetradic_Palatini_action wikiPageWikiLink Frame_fields_in_general_relativity.
- Tetradic_Palatini_action wikiPageWikiLink General_relativity.
- Tetradic_Palatini_action wikiPageWikiLink Holst_action.
- Tetradic_Palatini_action wikiPageWikiLink Plebanski_action.
- Tetradic_Palatini_action wikiPageWikiLink Ricci_curvature.
- Tetradic_Palatini_action wikiPageWikiLink Riemann_curvature_tensor.
- Tetradic_Palatini_action wikiPageWikiLink Scalar_curvature.
- Tetradic_Palatini_action wikiPageWikiLink Self-dual_Palatini_action.
- Tetradic_Palatini_action wikiPageWikiLink Spin_connection.
- Tetradic_Palatini_action wikiPageWikiLinkText "Tetradic Palatini action".
- Tetradic_Palatini_action wikiPageWikiLinkText "tetradic Palatini action".
- Tetradic_Palatini_action date "May 2013".
- Tetradic_Palatini_action reason "No indication in what context this equation is of any use, nor who developed it.".
- Tetradic_Palatini_action wikiPageUsesTemplate Template:Confusing.
- Tetradic_Palatini_action wikiPageUsesTemplate Template:Main.
- Tetradic_Palatini_action wikiPageUsesTemplate Template:Reflist.
- Tetradic_Palatini_action subject Category:General_relativity.
- Tetradic_Palatini_action comment "The Einstein–Hilbert action for general relativity was first formulated purely in terms of the space-time metric. To take the metric and affine connection as independent variables in the action principle was first considered by Palatini. It is called a first order formulation as the variables to vary over involve only up to first derivatives in the action and so doesn't over complicate the Euler–Lagrange equations with terms coming from higher derivative terms.".
- Tetradic_Palatini_action label "Tetradic Palatini action".
- Tetradic_Palatini_action sameAs Q17160411.
- Tetradic_Palatini_action sameAs m.0v3dfhk.
- Tetradic_Palatini_action sameAs Q17160411.
- Tetradic_Palatini_action wasDerivedFrom Tetradic_Palatini_action?oldid=654519514.
- Tetradic_Palatini_action isPrimaryTopicOf Tetradic_Palatini_action.