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• W2908087590 abstract "In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In the literature two such equations have been suggested: the one by Rutz and the one by one of the authors. Here we employ the method of canonical variational completion to show that Rutz equation can not be obtained from a variation of an action and that its variational completion yields the latter field equations. Moreover, to improve the mathematical rigor in the derivation of the Finsler gravity field equation, we formulate the Finsler gravity action on the positive projective tangent bundle. This has the advantage of allowing us to apply the classical variational principle, by choosing the domains of integration to be compact and independent of the dynamical variable. In particular in the pseudo-Riemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor." @default.
• W2908087590 created "2019-01-11" @default.
• W2908087590 creator A5000337805 @default.
• W2908087590 creator A5026846149 @default.
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• W2908087590 date "2019-09-20" @default.
• W2908087590 modified "2023-10-18" @default.
• W2908087590 title "Finsler gravity action from variational completion" @default.
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• W2908087590 doi "https://doi.org/10.1103/physrevd.100.064035" @default.
• W2908087590 hasPublicationYear "2019" @default.
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