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In this work, the collapsing process of a spherically symmetric star, made ofdust cloud, is studied in Ho\v{r}ava Lifshitz gravity in the background ofChaplygin gas dark energy. Two different classes of Chaplygin gas, namely, Newvariable modified Chaplygin gas and generalized cosmic Chaplygin gas areconsidered for the collapse study. Graphs are drawn to characterize the natureand to determine the possible outcome of gravitational collapse. A comparativestudy is done between the collapsing process in the two different dark energymodels. It is found that for open and closed universe, collapse proceeds withan increase in black hole mass, the only constraint being that, relativelysmaller values of $\Lambda$ has to be considered in comparison to $\lambda$.But in case of flat universe, possibility of the star undergoing a collapse inhighly unlikely. Moreover it is seen that the most favourable environment forcollapse is achieved when a combination of dark energy and dark matter isconsidered, both in the presence and absence of interaction. Finally, it is tobe seen that, contrary to our expectations, the presence of dark energy doesnot really hinder the collapsing process in case of Ho\v{r}ava-Lifshitzgravity.

Gravitational Collapse With Dark Energy And Dark Matter In Ho\v{r}ava-Lifshitz Gravity