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Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

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Abstract

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity.

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Notes

  1. By x=(x i) we denote local coordinates on V (indices i,j,k… and a,b,c… are coordinate or abstract ones which may take values 1, 2, 3, 4).

  2. Various nonhomogeneous generating functions (for instance, regular Lagrangians) and with other type homogeneity are also considered in modern literature.

  3. We consider that readers are familiar with basic concepts and constructions for the geometry of Lorentz manifolds and Finsler spaces; in this letter, we can not provide, explain and motivate all results and methods.

  4. For simplicity, we shall consider solutions with trapping on velocity type coordinate y 5, but the constructions can be performed in a similar for other fiber variables.

  5. In our works on GR and noncommutative, metric–affine, supersymmetric, string, brane, generalized Finsler etc extensions [31–38, 55–57], we provided examples when the fundamental equations (4), split into certain sub-systems of nonlinear partial differential equations (NPDE) which can be integrated in very general forms.

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Acknowledgements

The research for this paper is partially supported by the Program IDEI, PN-II-ID-PCE-2011-3-0256. I’m grateful for former collaboration and/or important discussions/correspondence relevant to this paper to P. Stavrinos, N. Mavromatos, C. Lämmerzahl, V. Perlick, S. Odintsov, and C. Castro.

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  1. Mathematical Physics Project IDEI, Alexandru Ioan Cuza University, UAIC, Alexandru Lapuşneanu street, nr. 14, Corpus R, Office 323, Iaşi, 700057, Romania

    Sergiu I. Vacaru

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  1. Sergiu I. Vacaru
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Correspondence to Sergiu I. Vacaru.

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Vacaru, S.I. Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories. Found Phys 43, 719–732 (2013). https://doi.org/10.1007/s10701-013-9711-y

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