Gravitational mass in asymptotically de Sitter space-times with compactified dimensions

Abstract

to be published in Phys. Rev. DWe 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.

The definition of mass in asymptotically de Sitter space-times

“…It is not straightforward to give an invariant definition of mass in an asymptotically de Sitter space-time containing mass in a compact region, due to problems arising from the existence of a cosmological event horizon. This is an old question that has been addressed by many authors, for example [1][2][3][4][5][6] among others. It is well known that the Komar mass [7] gives an ambiguous answer: if the Komar two-form associated with rotations is normalised so as to give the same angular momentum as that of the Arnowitt-Deser-Misner (ADM) formalism [8] then the two-form associated with time translations gives a value for the mass that differs from the ADM mass by a factor of two.…”