1992/11/13 by Jacob D. Bekenstein · 21 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #Conformal field theory #Conformal geometry #Conformal map #Cosmology and Gravitation Theories #Curvature #Differential geometry #Equivalence principle (geometric) #Fundamental theorem of Riemannian geometry #Geometry #Gravitation #Gravitational field #Mathematics #Microtubule and mitosis dynamics #Physics #Riemannian geometry #Scalar curvature #String theory #Theoretical physics #Transformation geometry #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.48.3641
published as Phys.Rev.D48:3641-3647,1993 · 15 pages, TeX
arxiv created 1992/11/13 · openalex publication_date 1993/10/15 · arxiv updated 2011/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The appearance of two geometries in a single gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between the two geometries allowed by physics? We study this question by supposing that the physical geometry on which matter dynamics takes place could be Finslerian rather than just Riemannian. An appeal to the weak equivalence principle and causality then leads us to the conclusion that the Finsler geometry has to reduce to a Riemann geometry whose metric, the physical metric, is related to the gravitational metric by a generalization of the conformal transformation involving a scalar field.