arXiv:2106.14220v1 [gr-qc] 27 Jun 2021 Singularity formation in radiating star with dark energy background Grishma Verma ∗ , Rajesh Kumar † , Keshav Ram Mishra ‡ Department of Mathematics and Statistics Deen Dayal Upadhyaya Gorakhpur University,Gorakhpur,INDIA. Abstract In this paper, we considered the gravitational collapse of a spherically symmetric radiating star consisting of perfect fluid (baryonic) in the back- ground of dark energy (DE) with equation of state   =   ( being non-zero constant parameter describing DE candidates). The effect of DE on the singularity formation has been discussed first separately (only DE present) and then combination of both baryonic and DE interaction. We have also showed that DE component   play important role in the forma- tion of Black-Hole(BH). In some cases the collapse of radiating star leads to black hole formation and in other cases it forms Naked-Singularity(or, eternally collapse). The present work is in itself remarkable to describe the effect of dark energy on singularity formation in radiating star. Key Words:- Dark Energy, Black Hole, Naked-Singularity, Radiating Star, Grav- itational collapse. 1 Introduction A massive star undergoes a continual gravitational collapse when the pressures inside the collapsing star become insufficient to balance the pull of gravity and the physics of it being crucial and interesting amongst astrophysicists. Using general relativistic techniques, it has been shown that the final fate of such a catastrophic collapse into singularity which may be either a black hole or a naked singularity, ∗ gris.grcosmo@gmail.com † rkmath09@gmail.com ‡ krmgkp1995@gmail.com 1