Higher-dimensional inhomogeneous composite fluids: energy conditions

Abstract

The energy conditions are studied, in the relativistic astrophysical setting, for higher-dimensional Hawking–Ellis Type I and Type II matter fields. The null, weak, dominant and strong energy conditions are investigated for a higher-dimensional inhomogeneous, composite fluid distribution consisting of anisotropy, shear stresses, non-vanishing viscosity as well as a null dust and null string energy density. These conditions are expressed as a system of six equations in the matter variables where the presence of the higher dimension $N$ is explicit. The form and structure of the energy conditions is influenced by the geometry of the $(N-2)$-sphere. The energy conditions for the higher-dimensional Type II fluid are also generated, and it is shown that under certain restrictions the conditions for a Type I fluid are regained. All previous treatments for four dimensions are contained in our work.