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The present paper deals with the gravitational collapse of an inhomogeneousspherical star consisting of dust fluid in the background of dark energycomponents with linear equation of state. We discussed the development ofapparent horizon to investigate the black-hole formation in gravitationalcollapsing process. The collapsing process is examined first separately fordust cloud and dark energy and then under the combined effect of dustinteracting with dark energy. It is obtained that when only dust cloud or darkenergy is present the collapse leads to the formation of black-hole undercertain conditions. When both of them are present, collapsing star does notform black-hole. However when dark energy is considered as cosmologicalconstant, the collapse leads to black hole formation.

Spherically Symmetric Gravitational Collapse Of Inhomogeneous Dust Cloud In The Background Of Dark Energy