Abstract
A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.
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References
G. Cavalleri and G. Spinelli,Nuov. Cim. 33B, 796 (1976).
G. Cavalleri and G. Spinelli,Nuov. Cim. 39B, 93 (1977).
I. W. Roxburgh and R. K. Tawakol,Gen. Rel. Grav. 10, 307 (1979).
G. S. Asanov,Nuov. Cim. 49B, 221 (1979).
G. S. Asanov, inProceedings of GR9, Jena (1980), to be published.
H. Rund,The Differential Geometry of Finsler Spaces (Springer-Verlag, Berlin, 1959).
A. H. Taub,Phys. Rev. 94, 1468 (1954).
J. L. Synge,Relativity: The General Theory (North-Holland, Amsterdam, 1960).
H. Rund,Arch. Rat. Mech. Anal. 71, 199 (1979).
R. Baumeister,Utilitas Mathematica 18, 189 (1980).
D. Lovelock and H. Rund,Tensors, Differential Forms and Variational Principles (Wiley, New York, 1975).
H. Rund, inTopics in Differential Geometry (Academic Press, New York, 1976), pp. 111–133.
G. S. Asanov,Found. Phys. 10, 855 (1980).
R. Baumeister,J. Math. Phys. 19, 2377 (1978).
G. S. Asanov,Rep. Math. Phys. 14, 237 (1978).
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Asanov, G.S. A Finslerian extension of general relativity. Found Phys 11, 137–154 (1981). https://doi.org/10.1007/BF00715202
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DOI: https://doi.org/10.1007/BF00715202