- Conservation Laws and Field Equations

2016 ◽  
pp. 27-54
Keyword(s):  
Conservation Laws ◽  
Field Equations

scholarly journals New cosmological solutions in hybrid metric-Palatini gravity from dynamical symmetries

2021 ◽  
pp. 2150100
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Conservation Laws ◽  
Integrable Systems ◽  
Functional Form ◽  
Analytic Solutions ◽  
Momentum Conservation ◽  
Field Equations ◽  
Dynamical Symmetries ◽  
Cosmological Solutions ◽  
Liouville Integrable

We investigate the existence of Liouville integrable cosmological models in hybrid metric-Palatini theory. Specifically, we use the symmetry conditions for the existence of quadratic in the momentum conservation laws for the field equations as constraint conditions for the determination of the unknown functional form of the theory. The exact and analytic solutions of the integrable systems found in this study are presented in terms of quadratics and Laurent expansions.

The Einstein field equations

2019 ◽  
pp. 52-58
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Geodesic Deviation ◽  
Fundamental Equations ◽  
Hilbert Action ◽  
Qualitative Discussion

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field equations from the Einstein-Hilbert action. The chapter contains a derivation of Noether’s theorem and the consequent conservation laws, and a brief discussion of generalizations of the Einstein-Hilbert action.

scholarly journals On the Mathematics of Coframe Formalism and Einstein–Cartan Theory—A Brief Review

Universe ◽  
2019 ◽  
Vol 5 (10) ◽  
pp. 206 ◽  
Author(s):  
Manuel Tecchiolli
Keyword(s):  
Conservation Laws ◽  
Gauge Fields ◽  
Field Equations ◽  
Principal Bundles ◽  
Bianchi Identities ◽  
Cartan Theory

This article is a review of what could be considered the basic mathematics of Einstein–Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities, and eventually, we will end up with Einstein–Cartan–Sciama–Kibble field equations and conservation laws in their implicit formulation.

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

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