Anti-Gravity Bounds and the Ricci Tensor

Abstract

Recently Penrose, Sorkin and Woolgar have developed a new technique for proving the positive mass theorem in general relativity. We extend their result to produce a new inequality relating the mass, electric and scalar charges in theories coupling to a dilaton in the usual way. Using a five dimensional formalism, our result provides new information not available from the existing techniques. The main result may be simply expressed as M + gΣ\ge { \sqrt{1+g^2} |Q| \over \sqrt {4πG} } . where `M' is the A.D.M. mass, `Q' is the electric charge, `Σ' the scalar charge and `g' is the dilaton coupling parameter.