General relativity without general relativity

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 GN 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 GN 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.