Integrable covariant law of energy-momentum conservation for a gravitational field with the absolute parallelism structure These conservation laws are used for the construction of the covariant equations of motion for test bodies with minimal and nonminimal coupling. We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. â–º Some different forms of Schwarzschild solutions are considered as simple examples of different boundary conditions.Ĭonservation laws and covariant equations of motion for spinning particles â–º Boundary conditions for this to be possible are considered and compared with the literature. Highlights: â–º In the paper ADM conserved quantities for GR are obtained from augmented conservation laws. The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest while, in view of their covariance, covariant conservation laws give the correct result in all cases. This determines explicitly the range in which standard techniques are equivalent to covariant conserved quantities. Then a number of independent sets of hypotheses that are sufficient (though not necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained.

International Nuclear Information System (INIS)įatibene, L. ADM pseudotensors, conserved quantities and covariant conservation laws in general relativity

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