Anti-Gravity Bounds and the Ricci Tensor

TL;DR

This paper extends recent techniques in general relativity to derive a new inequality linking mass, electric charge, and scalar charge in dilaton theories, using a five-dimensional formalism for novel insights.

Contribution

It introduces a new inequality relating mass, electric, and scalar charges in dilaton theories, extending existing positive mass theorem techniques with a five-dimensional approach.

Findings

Derived a new inequality: M + gΣ ≥ (√(1+g²)|Q|) / √(4πG)

Extended Penrose, Sorkin, Woolgar's methods to dilaton theories

Provided a novel five-dimensional formalism for these inequalities

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 + g\Sigma \ge { \sqrt{1+g^2} |Q| \over \sqrt {4\pi G} } . where `M' is the A.D.M. mass, `Q' is the electric charge, `\Sigma' the scalar charge and `g' is the dilaton coupling parameter.