Journal ArticleDOI
A variational principle giving gravitational “superpotentials,” the affine connection, Riemann tensor, and Einstein field equations
John Stachel,John Stachel +1 more
TLDR
In this paper, a first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensorRμνkλ in terms of the affine connection and metric, and the definition of a set of gravitational superpotentials closely connected with the Komar conservation laws.Abstract:
A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensorRμνkλ in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational “superpotentials” closely connected with the Komar conservation laws [7]. Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational “superpotentials”.read more
Citations
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Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint
TL;DR: In this paper, a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently is investigated. And the outcome of this procedure is a gravitational theory formulated in a volume-preserving space-time (i.e., with torsion and trace-free nonmetricity).
Journal ArticleDOI
Conformal and projective structures in general relativity
TL;DR: In this article, it is suggested that compatible conformal and projective structures are the basic space-time structures in general relativity, with the symmetry group restricted to unimodular diffeomorphisms.
Journal ArticleDOI
Conservation laws for energy and momentum in curved spaces
TL;DR: In this paper, continuity equations for the energy and momentum of the gravitational field were constructed in arbitrary Riemannian 4-spaces, which could be interpreted as conservation laws for the GFG.
Journal ArticleDOI
A Note on Lagrangians and Lovelock-Rund’s Identities
TL;DR: In this article, the authors construct continuity equations in arbitrary Riemannian 4-space, which could be interpreted as conservation laws for the energy and momentum of the gravitational field.
References
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Journal ArticleDOI
The classical theory of fields
TL;DR: The principle of relativity Relativistic mechanics Electromagnetic fields electromagnetic waves as discussed by the authors The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation
Journal ArticleDOI
An Approach to Gravitational Radiation by a Method of Spin Coefficients
Ezra T. Newman,Roger Penrose +1 more
TL;DR: In this paper, a spinor affine connection is proposed for general relativity by means of a tetrad or spinor formalism, which is applied to two problems in radiationtheory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.
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Covariant conservation laws in general relativity
TL;DR: In this paper, a set of covariant conservation laws is constructed in the general theory of relativity, and their relationship to the generators of infinitesimal coordinate transformations is indicated.
Journal ArticleDOI
Conservation Laws in General Relativity
TL;DR: In this paper, the conservation laws of the Lagrangian were examined from the transformation properties of Lagrangians and the energy-momentum complex obtained has mixed indices, whereas a symmetric quantity is required for the definition of angular momentum.