Higher dimensional heat conducting models with vanishing shear

Abstract

A shear-free relativistic fluid with nonzero heat flux is studied by examining the higher dimensional spherically symmetric shear-free interior spacetime. The model is a heat conducting fluid undergoing dissipation. The Einstein field equations are generated in arbitrary dimensions for such a fluid and the assumption of isotropic fluid pressure realises a coupled partial differential equation in the gravitational potentials. We generate exact solutions to the isotropic pressure condition equation which represents a generalisation of the known four dimensional solutions. We also illustrate that the matter variables are physically well behaved and that the energy conditions are satisfied which is essential for constructing a complete and physically viable model in the context of radiating stars with vanishing shear.