Finsler gravity action from variational completion
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 pseudoRiemannian case, the vacuum field equation becomes equivalent to the vanishing of the Ricci tensor.
 Publication:

Physical Review D
 Pub Date:
 September 2019
 DOI:
 10.1103/PhysRevD.100.064035
 arXiv:
 arXiv:1812.11161
 Bibcode:
 2019PhRvD.100f4035H
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 22 pages + 11 pages auxiliary material, no figures, LaTeX