Shear-free models for relativistic fluids with heat flow and pressure isotropy.

Abstract

We model the interior dynamics of a relativistic radiating fuid in a nonstatic spher- ically symmetric spacetime. The matter distribution takes the form of an imperfect

fuid with a nonvanishing radially directed heat flux. The fluid pressure is isotropic and the spherically symmetric spacetime manifold is described by a shear-free line el- ement. In our investigation, the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. We examine this governing equation by imposing vari- ous forms for these potentials and review classes of physically acceptable models that are applicable in relativistic astrophysics. Several new classes of new exact solutions to the condition of pressure isotropy are also found. A comparison of our solutions with earlier well known results is undertaken. A physical analysis of two of the new models is performed where the spatial and temporal evolution of the matter and grav- itational variables are probed. We demonstrate that the fluid pressure, energy density and heat flux are regular and well behaved for both models throughout the interior, and our results indicate that one of the models is consistent with the well established core-envelope framework for compact stellar scenarios. We also analyse the energy conditions for the radiating fluid and demonstrate consistent behaviour, with only the dominant condition being violated. Finally, an analysis of the relativistic thermody- namics of two solutions is undertaken in the Israel-Stewart theory and the temperature profiles for both the noncausal and causal cases are presented.