Negative mass in general relativity

Mechanics is considered in a universe containing negative mass. Demanding (i) conservation of momentum, (ii) principle of equivalence, (iii) no runaway motions, (iv) no Schwarzschild black holes, and (v) the inertial and active gravitational masses of a body shall have the same sign, we find thatall mass must be negative. Some properties of such a universe are investigated. We show that a neutral spherical body of arbitrarily small size is possible, and observers external to it can communicate with each other by light rays without horizon problems. There are no cosmological models with a power-law big bang, and there is an abundance of nonsingular models. Like electric charges would attract each other, and unlike ones would repel. This could produce stars and galaxies held together by charge and not gravity. The investigation does not suggest any reason why mass in the real universe should be positive.