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Hamiltonian cosmology and gravitational solitons: A variational outlook
Phys. Rev. D 26, 3354 – Published 15 December, 1982
DOI: https://doi.org/10.1103/PhysRevD.26.3354
Abstract
A general procedure is applied for finding the possible variational principle of a given nonlinear system of partial differential equations. In particular, attention is focused on Hamiltonian homogeneous cosmologies and gravitational solitons. In the first case, it is found that a variational principle exists if and only if the model is of class A, thus complementing previous results of MacCallum and Taub. In the second case, it is shown that the pertinent system arises from a variational principle; furthermore, the explicit form of the Lagrangian is given. Owing to the structure of the Lagrangian an outstanding first integral is determined.
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