The Relation between Physical and Gravitational Geometry

Details The Relation between Physical and Gravitational Geometry The Relation between Physical and Gravitational Geometry

1992-11-13

arxiv.org/abs/gr-qc/9211017v1

Phys.Rev.D48:3641-3647,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, TeX

Scientific paper

10.1103/PhysRevD.48.3641

The appearance of two geometries in one and the same 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 take place could be Finslerian rather than just Riemannian. An appeal to the weak equivalence principle and causality then leads us 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.

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