Abstract
Spinning equations of Finslerian gravity, the counterpart of the Mathisson-Papapetrou spinning equations of motion are obtained. Two approaches of Finslerian geometries are formulated and discussed, the Cartan-Rund and Finsler-Cartan ones, as well as their corresponding spinning equations. The significance of the nonlinear connection and its relevance on spinning equations is noticed, and their deviations are examined.
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REFERENCES
E. Cartan, Les Spaces de Finsler (Paris, Herman, 1935); S. F. Rutz, and F. M. Pavia, Finslerian Geometry (Ed. P. L. Antonelli, Kluwer Academic Publisher, 2000).
C. C. Perelman, PAIJ 2, issue 6 (2018).
S. Chern, Sci. Rep. Nat. Tsing Hua Univ., Ser. A 5, 59 (1948);
S. Chern, Sci. Rep. Nat. Tsing Hua Univ., Ser. A 5, 59 (1948); D. Bao, S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Geometry (Graduate Text in Mathematics 200, Springer, 1959); H. Rund, The Differential Geometry of Finsler Spaces (Springer-Verlag, 1959).
M. Anastasici and H. Shimada, Finslerian Geometry (Ed. P. L. Antonelli, Kluwer Academic Publisher, 2000).
L. Bubuianu and S. Vacaru, Eur. Phys J. C 78, 969 (2018);
L. Bubuianu and S. Vacaru, Eur. Phys J. C 78, 969 (2018); S. Vacaru, arXiv: 1801.06444.
S. L. Bazanski J. Math. Phys. 30, 1018 (1989).
M. E. Kahil, J. Math. Phys. 47, 052501 (2006).
Magd E. Kahil, Grav. Cosmol. 24, 83 (2018).
Magd E. Kahil, ADAP 3, 136 (2018).
Magd E. Kahil, Grav. Cosmol. 25, 268 (2019).
M. Pavšič and Magd E. Kahil, Open Physics 10, 414 (2012).
M. Heydrai-Fard, M. Mohseni, and H. R. Sepanigi, Phys. Lett. B 626, 230 (2005).
D. Bini and A Geralico, Phys. Rev. D 84, 104012 (2011); arXiv: 1408.4952.
A. Papapetrou, Proc. Roy. Soc. London A 209, 248 (1951).
F. W. Hehl, J. D. Mc Grea, E. W. Mielke, and Y. Ne’emann, Phys. Rep. 258, 1 (1995).
R. Miron and M. Anastasiei, Vector Bundles and Lagrange Spaces (Balkan Press, 1997); S. Vacaru, Phys. Lett. B 690, 224 (2010);
R. Miron and M. Anastasiei, Vector Bundles and Lagrange Spaces (Balkan Press, 1997); S. Vacaru, Phys. Lett. B 690, 224 (2010); S. Vacaru, P. Stavrinos, E. Gaburov, and D. Gonta, Differential Geometry —Dynamical Systems (Monograph 7, Geometry, Balkan Press, 2006); gr-qc/0508023.
J. Sklakla and M. Visser, arXiv: 1008.0689.
H. Brandt, Found. Physics Letters 4, No. 6 (1991).
C. Castro, hep-th/0211053.
H. Brandt, Finslerian Geometry (Ed. P. L. Antonelli, Kluwer Academic Publishers, 2000).
A. K. Aringazin and V. Dzhunushaliev, arXiv: 1303.0912.
P. D. Collins, A. D. Martin, and E. J. Squires Particle Physics and Cosmology (John Wiley and Sons, 1989).
M. I. Wanas, M. E. Kahil, and Mona M. Kamal, Grav. Cosmol. 22, 345 (2016).
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Kahil, M.E. Spinning Equations for Objects of Some Classes in Finslerian Geometry. Gravit. Cosmol. 26, 241–248 (2020). https://doi.org/10.1134/S0202289320030093
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DOI: https://doi.org/10.1134/S0202289320030093