We investigate the gravitational collapse of a gravitational bounded object constituted of dust cloud and dark energy. We considered the the effects of homogenous and isotropic fluid on newly suggested 4D limit for Einstein-Gauss-Bonnet gravity(EGB) (For detail about EGB gravity, arXiv:1905.03601v3). For this purpose, we consider the gravitational collapse of gravitational object made of dust cloud ρDM in the background of dark energy, p = wρ with (w < −1/3). We illustrate that the procedure is qualitatively equivalent to the scenario of theory of Einstein for the collapse of the gravitational object composed of homogeneous dust. Further, we consider the collapse for dark energy by considering the equation of state p = wρ to find that black hole also may form in EGB case, which predict that end state of gravitational collapse in EGB case is consistent with results carried out in pure Einstein’s gravity theory.
We have discussed two separate case, first, gravitational collapse of dust cloud in the context of EGB, in the second case, gravitational collapse of dark energy in EGB background. It is found that, gravitational collapse leads to formation of black hole in both cases. It is also worth mentioning that, end state of gravitational collapse in EGB context is same as in pure Einstein's gravity. Here, in this study dark matter refer to dust cloud, a matter with zero pressure.
