alexa Modified Einstein and Finsler Like Theories on Tangent Loren tz Bundles
Mathematics

Mathematics

Journal of Physical Mathematics

Author(s): Panayiotis Stavrinos Olivia V

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We study modifications of general relativity, GR, with nonli near dispersion relations which can be ge- ometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravita- tional Lagrange density functionals f ( R , T ,F ) with generalized/ modified scalar curvature R , trace of matter field tensors T and modified Finsler like generating function F . In particular, there are defined extensions of GR with extra dimensional "velocity/ momentum" coordina tes. For four dimensional models, we prove that it is possible to decouple and integrate in very general forms the gravitational fields for f ( R , T ,F ) – modified gravity using nonholonomic 2+2 splitting and nonho lonomic Finsler like variables F . We study the modified motion and Newtonian limits of massive test part icles on nonlinear geodesics approximated with effective extra forces orthogonal to the four–velocity . We compute the constraints on the magnitude of extra–accelerations and analyze perihelion effects and pos sible cosmological implications of such theories. We also derive the extended Raychaudhuri equation in the frame work of a tangent Lorentz bundle. Finally, we speculate on effective modelling of modified theories by gene ric off–diagonal configurations in Einstein and/or MGTs and Finsler gravity. We provide some examples for modifi ed stationary (black) ellipsoid configurations and locally anisotropic solitonic backgrounds.

This article was published in Int. J. Mod. Phys and referenced in Journal of Physical Mathematics

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