On the Development of the Covariant Formulation of the Conservation Laws of General Relativity

1966 ◽  
Vol 7 (6) ◽  
pp. 975-976 ◽  
Author(s):  
W. R. Davis ◽  
M. K. Moss
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Covariant Formulation

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

scholarly journals Quasilocal conservation laws in cosmology: A first look

2020 ◽  
Vol 29 (14) ◽  
pp. 2043029
Author(s):  
Marius Oltean ◽  
Hossein Bazrafshan Moghaddam ◽  
Richard J. Epp
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Conservation Laws ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Fluid Matter ◽  
Stress Energy Momentum Tensor

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

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