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On the Theory of Gravitational Field in Finsler Spaces ‐ III
Author(s) -
Ikeda Satoshi
Publication year - 1990
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.19905020102
Subject(s) - gravitational field , physics , field (mathematics) , einstein , gravitation , space (punctuation) , field equation , vector field , classical field theory , mathematical physics , base (topology) , classical mechanics , mathematical analysis , mathematics , pure mathematics , philosophy , mechanics , linguistics
Abstract From the vector bundle‐like standpoint, the Finslerian gravitational field is regarded as the total space of the vector bundle whose fibre is the internal ( y )‐field spanned by vectors { y } (i.e., the so‐called internal space spanned by { y }) and whose base is the external ( x )‐field spanned by points { x } (i.e., the Einstein's gravitational field). Along this line, in this paper, different from a previous paper [1], the so‐called mapping process of the ( y )‐field on the ( x )‐field is not taken into account and following Miron's method [2, 3], the Finslerian field equations will be derived from the Einstein's field equation for the total space. Some physical considerations will be made on those field equations.