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On the Theory of Gravitational Field in Finsler Spaces
Author(s) -
Ikeda Satoshi
Publication year - 1987
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19874990803
Subject(s) - physics , gravitational field , field (mathematics) , connection (principal bundle) , gravitation , metric (unit) , riemann hypothesis , mathematical physics , pure mathematics , classical mechanics , mathematics , geometry , operations management , economics
Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g λχ ( x, y ) = γ λχ ( x ) + h λχ ( x, y ) is proposed, where γ λχ denotes the Riemann metric of Einstein's gravitational field, while h λχ the Finsler metric induced by the Riemann metric h ij ( y ) of the internal field; The intrinsic behaviour of the internal variable y , which is expressed as ȳ i = K j i ( x, y ) y j in the internal field, is grasped by the Finslerian parallelism δ y i (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy χ = e i x ( x ) δ y i . The whole metrical Finsler connection D for g λχ (i.e., Dg λχ = 0) is determined by taking account of the intrinsic behaviour δ y χ .