Gravitational Mass in Asymptotically de Sitter Space-Times with Compactified Dimensions

TL;DR

This paper defines gravitational mass in asymptotically de Sitter space-times with compactified dimensions, revealing conditions for negative mass and exploring implications for matter and elementary fermions.

Contribution

It introduces a new definition of gravitational mass in these space-times and demonstrates the possibility of negative mass without horizon or momentum constraints.

Findings

Mass can be negative for matter beyond the horizon or with large momentum.

Examples show negative energy states in higher dimensions without horizon or momentum.

Elementary fermions cannot exist in the constructed examples.

Abstract

We define gravitational mass in asymptotically de Sitter space-times with compactified dimension. It was shown that the mass can be negative for space-time with matter spreading beyond the cosmological horizon scale or large outward `momentum' in four dimension. We give simple examples with negative energy in higher dimensions even if the matter is not beyond horizon or system does not have large `momentum'. They do not have the lower bound on the mass. We also give a positive energy argument in higher dimensions and realise that elementary fermion cannot exist in our examples.