An embedding for general relativity with variable rest mass

Abstract

There is considerable interest currently in theories of gravity where rest masses vary slowly with time. A new theory of this type is proposed which is believed to be superior to others, and which contains Einstein's theory embedded within it. The theory is five dimensional, where the extra coordinate isx4=Gm/c2 (G is the Newtonian gravitational parameter,c the velocity of light, andm the mass). The theory reduces to Einstein's ifw=(G/c3)dm/dt=0 and the fifth dimension is absent. The theory agrees with observation providedw≪1, but the size ofw in the real world can only be determined by experiment.