A variational principle giving gravitational 'superpotentials,' the affine connection, Riemann tensor, and Einstein field equations

Details A variational principle giving gravitational 'superpotentials,' the affine connection, Riemann tensor, and Einstein field equations A variational principle giving gravitational 'superpotentials,' the affine connection, Riemann tensor, and Einstein field equations

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..705s&link_type=abstract

General Relativity and Gravitation, vol. 8, Aug. 1977, p. 705-712.

Physics

2

Einstein Equations, Field Theory (Physics), Gravitational Fields, Variational Principles, Lagrangian Equilibrium Points, Riemann Manifold, Tensors, Topology

Scientific paper

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor 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 (1959) conservation laws. 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.'

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