This was put forth by Einstein. As the density of space-time increases, time slows down because if the amount of energy stays the same and the ambient mass becomes greater, the motion slows down. You don't get energy from no-where and no mass magically pops into existence, if more energy is required to move at the same rate and there is no extra energy applied, the rate will slow down. So now we have enough information about the space-time to be useful. Any mass will produce a higher density in the surrounding space-time as it looses energy, and all of the density gradients will combine to produce acceleration of the objects towards each other.
Matter begins as a compressed zone and anti-matter begins as a rareified zone.