Towards a gravitation theory in Berwald-Finsler space

LI Xin; CHANG Zhe

doi:10.1088/1674-1137/34/1/005

Chinese Physics C> 2010, Vol. 34> Issue(1) : 28-34 DOI: 10.1088/1674-1137/34/1/005

Towards a gravitation theory in Berwald-Finsler space

LI Xin ^, ,
CHANG Zhe

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Abstract：
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is
nonsymmetric in general. This indicates that the local Lorentz invariance is violated.

References

[1]

. Cohen A G, Glashow S L. Phys. Rev. Lett., 2006, 97:0216012. Kostelecky V A, Samuel S. Phys. Rev. D, 1989, 39: 6833. Damour T, Polyakov A M. Nucl. Phys. B, 1994, 423: 5324. Amelino-Camelia G, Ellis J R, Mavromatos N E, Nanopou-los D V, Sarkar S. Nature, 1998, 393: 7635. Gambini R, Pullin J. Phys. Rev. D, 1999, 59: 1240216. Alfaro J, Morales-Tecotl H A, Urrutia L F. Phys. Rev.Lett., 2000, 84: 2318; Phys. Rev. D, 2002, 65: 1035097. Hayakawa M. Phys. Lett. B, 2000, 478: 394; hep-th/99121678. Mocioiu I, Pospelov M, Roiban R. Phys. Lett. B, 2000, 489:3909. Carroll S M, Harvey J A, Kostelecky V A, Lane C D,Okamoto T. Phys. Rev. Lett., 2001, 87: 14160110. Anisimov A, Banks T, Dine M, Graesser M. Phys. Rev. D,2002, 65: 08503211. Burgess C P, Cline J, Filotas E, Matias J, Moore G D. J. High Energy Phys., 2002, 03: 04312. Girelli F, Liberati S, Sindoni L. Phys. Rev. D, 2007, 75:06401513. Gibbons G W, Gomis J, Pope C N. hep-th/0707.217414. Battistoni G et al. Phys. Lett. B, 2005, 615: 1415. Randers G. Phys. Rev., 1941, 59: 19516. Yasuda H, Shimada H. Rep. on Math. Phys., 1977, 11: 34717. BAO D, Lackey B. Nonlinear Analysis, 1999, 38: 2718. Hrimiuc D, Shimada H. Nolinear World, 1996, 3: 613; Ten-sor, N.S., 1996, 58: 4819. Sabau V S, Shimada H. Rep. Math. Phy., 2001, 47: 3120. CHANG Z, LI Xin. hep-th/0711.005621. Kostelecky V A. Phys. Rev. D, 2004, 69: 10500922. Chern S S. Sci. Rep. Nat. Tsing Hua Univ. Ser. A, 1948,5: 95; Selected Papers, vol. /, 194, New York: Springer,198923. BAO D, Chern S S, SHEN Z. An introduction to Riemann-Finsler geometry, Graduate Texts in Mathmatics, 200:New York: Springer, 200024. Akbar-Zadeh H. Acad. Roy. Belg. Bull. Cl. Sci., 1988,74(5): 28125. Kikuchi S. Tensor, N.S., 1979, 33: 242

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LI Xin and CHANG Zhe. Towards a gravitation theory in Berwald-Finsler space[J]. Chinese Physics C, 2010, 34(1): 28-34. doi: 10.1088/1674-1137/34/1/005

LI Xin and CHANG Zhe. Towards a gravitation theory in Berwald-Finsler space[J]. Chinese Physics C, 2010, 34(1): 28-34. doi: 10.1088/1674-1137/34/1/005 shu

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Received: 2009-02-26
Revised: 2009-03-09

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Towards a gravitation theory in Berwald-Finsler space

Corresponding author: LI Xin,

Received Date: 2009-02-26

Accepted Date: 2009-03-09

Available Online: 2010-01-05

Abstract:

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is
nonsymmetric in general. This indicates that the local Lorentz invariance is violated.

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Towards a gravitation theory in Berwald-Finsler space

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