Physics – Mathematical Physics
Scientific paper
2010-10-26
General Relativity and Gravitation 44 (2012) 1015-1042
Physics
Mathematical Physics
latex2e, 11pt, 35 pages, v3 accepted to GRG and modified following referee's recommendations
Scientific paper
10.1007/s10714-011-1324-1
We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein-Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Ho\v{r}ava-Lifshitz, HL, and/or Einstein's general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Ho\v{r}ava-Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.
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