## On the physical viability of horizon-free collapse.

##### Abstract

The so-called Cosmic Censorship Conjecture has drawn widespread attention amongst
astrophysicists and particle physicists. In particular, the end-state of gravitational collapse
of a bounded matter distribution is a source of much debate with the discovery
of naked singularities resulting from the continued gravitational collapse of reasonable
matter distributions. One of the first attempts at investigating the final outcome of
gravitational collapse of a stellar object was undertaken by Oppenheimer and Snyder
in 1939. Their model was highly idealised and focussed on a dust sphere contracting
under its own gravity. With the discovery of the Vaidya solution, it became possible
to model stars emitting energy to the exterior spacetime. In this dissipative model,
the exterior spacetime is nonempty and the collapsing stellar body is enveloped by a
zone of null radiation. The smooth matching of the interior spacetime to the Vaidya
exterior was achieved by Santos in 1985. It was then possible to model radiating stars
undergoing gravitational collapse. The energy momentum tensor for the interior stellar
fluid was modelled on more realistic physics and was extended to include heat flux,
neutrino transport, shear, pressure anisotropy, bulk viscosity and the electromagnetic
field. It has been shown 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.
In this study we investigate a radiating stellar model proposed by Banerjee et al
(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. Our approach is more general than the one proposed
by Banerjee et al as they fix the gravitational potentials for the interior line element
by making ad-hoc assumptions. A consequence of their model is that it undergoes
horizon–free collapse. We start off with the fact that the horizon never forms throughout
the collapse process. This restricts the gravitational behaviour of the model. We
utilise the boundary condition to determine the temporal evolution of the model. As
a result, we obtain new collapsing models in which the horizon never forms.
In order to investigate the physical viability of our generalised BCD model we
analyse the luminosity profile and the temperature profiles within the framework of
extended irreversible thermodynamics. We highlight interesting physical features of
our results.