Yilmaz Cancels Newton

Abstract

A central tenet of the new theory of gravity proposed by H. Yilmaz is the inclusion of a gravitational stress-energy tensor $-{t_μ}^ν$ along with the matter stress-energy tensor ${T_μ}^ν$ on the right hand side of the Einstein field equations. This change does not effect the Newtonian limit of the field equations since these terms are quadratic in potential gradients. {}From the Bianchi identities, however, important changes appear in any equations of motion consistent with these field equations. For matter described as a perfect fluid, and with Yilmaz's choice of signs when introducing these quadratic terms, we find that the Euler hydrodynamic equation in the Newtonian limit is modified to remove all gravitational forces. This allows, e.g., a solar system in which the Sun and the planets are permanently at rest, but does not explain how fluid bodies such as the Sun or Jupiter could form or be prevented from dispersing.