General relativity without general relativity

Abstract

Recently one of us proposed a general theory of variable rest masses (VMT) compatible with post-Newtonian solar-system experiments for a wide range of its two parameters $r$ and $q$, provided the asymptotic value of its fundamental field $f$ is in a certain narrow range. Here we show that the stationary matter-free black-hole solutions of the VMT are identical to those of general relativity. In addition, for $r<0$ and $q>0$ (part of the range mentioned), relativistic neutron-star models in the VMT are very similar to their general-relativistic counterparts. Thus experimental discrimination between the two theories in the strong-field limit seems unfeasible. We show that in all isotropic cosmological models of the VMT capable of describing the present epoch, the Newtonian gravitational constant ${G}_{N}$ is positive throughout the cosmological expansion. There exist nonsingular VMT cosmological solutions; this is an advantage the VMT has over general relativity. For $r<0$ and $q>0$ all VMT cosmological models converge to their general-relativistic analogs at late times. As a consequence the asymptotic $f$ attains just the required values to guarantee agreement of the VMT with post-Newtonian experiments. The VMT with $r<0$ and $q>0$ predicts a positive Nordtvedt-effect coefficient. It also predicts that ${G}_{N}$ is currently decreasing on a time scale which could be long compared to the Hubble time. Verification of these predictions would rule out general relativity; its most natural replacement would be the VMT with $r<0$ and $q>0$, and not a generic scalar-tensor theory. The success of general relativity in most respects could then be understood because the VMT with $r<0$ and $q>0$ mimics it. Because of this, general relativity could still be used, for most purposes, as a good approximation to the correct gravitational theory.