Two variational principles for second order materials within general relativity

1975 ◽  
Vol 106 (1) ◽  
pp. 315-327 ◽  
Author(s):  
Mario Pitteri
Keyword(s):  
General Relativity ◽  
Variational Principles ◽  
Second Order

Quadratic Lagrangians and gauge-invariance in covariant field theories

1960 ◽  
Vol 56 (3) ◽  
pp. 247-251 ◽  
Author(s):  
G. Stephenson
Keyword(s):  
General Relativity ◽  
Gauge Transformation ◽  
Gauge Invariance ◽  
Variational Principles ◽  
Scalar Function ◽  
Field Equations ◽  
General Group ◽  
Metric Tensor ◽  
Invariance Properties ◽  
Image Position

The idea of gauge-invariance in general relativity was first introduced by Weyl(1) who proposed that the field equations of gravitation should be invariant, not only under the general group of coordinate transformations, but also under the gauge-transformationwhere is the symmetric metric tensor, is the symmetric affine connexion and λ(x8) is an arbitrary scalar function of the coordinates. In this way it was possible to introduce into the theory a four-vector Ak which in consequence of (1·1) transformed assuch that the six-vector remained an invariant quantity under the gauge-transformation. It was Weyl's hope that by widening the invariance properties gauge-transformation. It was Weyl's hope that by widening the invariance properties of general relativity in this way the vector Ak and its associated six-vector Fik could be interpreted as representing the electromagnetic field. However, no obvious or unique way of doing this was found. More recently (see Stephenson (2,3) and Higgs (4)) gaugeinvariant variational principles formed from Lagrangians quadratic in the Riemann—Christoffel curvature tensor and its contractions have been discussed by performing the variations with respect to the symetric and symetric independently (following the palatini method).

The first and second order formulations of general relativity

Supergravity ◽  
2012 ◽  
pp. 171-184
Author(s):  
Daniel Z. Freedman ◽  
Antoine Van Proeyen
Keyword(s):  
General Relativity ◽  
Second Order

Variational principles and second-order Lagrangian densities

1994 ◽  
Vol 49 (2) ◽  
pp. 129-134 ◽  
Author(s):  
G J N Brown ◽  
S F C O'Rourke ◽  
D S F Crothers
Keyword(s):  
Variational Principles ◽  
Second Order ◽  
Lagrangian Densities

scholarly journals Zel’dovich-type approximation for an inhomogeneous universe in general relativity: Second-order solutions

1996 ◽  
Vol 53 (12) ◽  
pp. 6881-6888 ◽  
Author(s):  
Heinz Russ ◽  
Masaaki Morita ◽  
Masumi Kasai ◽  
Gerhard Börner
Keyword(s):  
General Relativity ◽  
Second Order ◽  
Inhomogeneous Universe ◽  
Type Approximation
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