Energy condition and cosmic censorship conjecture in the perfect fluid collapse

The hypothesis of cosmic censorship plays a crucial role in classical general relativity, as an aspect of the strong version it expresses that naked singularities would never occur from the black hole singularity. In this paper, we will present how energy conditions prohibit forming the local naked singularity in the spherical perfect fluid collapse, and thus we get one step closer to the strong cosmic censorship conjecture proof. We also show that this result can be extended to the cosmological constant background.