Post-Newtonian approximation of a new theory of gravity

Abstract

The post-Newtonian approximation is developed for a new theory of gravity based on a Hermitian metric gμν. The approximation gives Newtonian theory in lowest order, but differs from general relativity in post-Newtonian order. The equations of motion, energy–momentum conservation, and perihelion precession are investigated. The equations of motion are derivable from the conservation laws of the energy–momentum tensor. A multipole expansion of the metric is formulated, and the PPN parameters α, β, and γ are found all to be unity. Several new parameters occur, most notably I, which is related to the number density of fermions of a system.