Causal temperature profiles in horizon - free collapse

The Cosmic Censorship Conjecture has continued to occupy center stage within the realms of relativistic astrophysics. The final outcome of the gravitational collapse of a star is still very much open to debate with the discovery of models admitting naked singularities.1,2 Various scenarios of gravitational collapse have been considered in which the energy momentum tensor is taken to be either a perfect fluid or an imperfect fluid with heat flux and anisotropic pressure.3,4,5 It is well known that the collapse of reasonable matter distributions always lead to the formation of a black hole in the absence of shear or in the case of homogeneous densities. It has been shown that shearing effects delay the formation of the apparent horizon by making the final stages of collapse incoherent thus leading to the generation of naked singularities.6 In this letter we revisit a radiating stellar model proposed by Banerjee et al7, (hereafter referred to as the BCD model) in which the horizon is never encountered. The interior matter distribution is that of an imperfect fluid with heat flux and the exterior spacetime is described by the radiating Vaidya metric.8 The junction conditions required for the smooth matching of the interior and exterior spacetimes across a four-dimensional time-like hypersurface are solved exactly.