Relation between physical and gravitational geometry
Jacob D. BekensteinDepartment of Physics, University of California at Santa Barbara, Santa Barbara, California 93106 and The Racah Institute of Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
1993en
ABI
Abstract
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.
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