scholarly journals Quasigroups, asymptotic symmetries, and conservation laws in general relativity

1997 ◽  
Vol 56 (12) ◽  
pp. R7498-R7502 ◽  
Author(s):  
Alexander I. Nesterov
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Asymptotic Symmetries

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

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 Energy–Momentum Pseudotensor and Superpotential for Generally Covariant Theories of Gravity of General Form

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 173
Author(s):  
Roman Ilin ◽  
Sergey Paston
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Wide Class ◽  
Equations Of Motion ◽  
General Covariance ◽  
Independent Variables ◽  
Theories Of Gravity ◽  
Generally Covariant ◽  
Derivatives Of ◽  
Mimetic Gravity

The current paper is devoted to the investigation of the general form of the energy–momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general covariance of the action without any restrictions on the order of derivatives of the independent variables in it or their transformation laws. As a result of the generalized Noether procedure, we obtain a recurrent chain of the equations, which allows one to express canonical pEMT as a divergence of the superpotential. The explicit expression for this superpotential is also given. We discuss the structure of the obtained expressions and the conditions for the derived pEMT conservation laws to be satisfied independently (fully or partially) by the equations of motion. Deformations of the superpotential form for theories with a change in the independent variables in action are also considered. We apply these results to some interesting particular cases: general relativity and its modifications, particularly mimetic gravity and Regge–Teitelboim embedding gravity.

Conservation laws in general relativity

1959 ◽  
Vol 13 (1) ◽  
pp. 237-240 ◽  
Author(s):  
C. Cattaneo
Keyword(s):  
General Relativity ◽  
Conservation Laws
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