Condition for Primordial Black Hole (PBH) formation in matter dominated era including inhomogeneity effect is derived with treating general relativity. We investigate how the inhomogeneity of density perturbation affects the formation of PBHs. Black hole formation is determined by comparing two characteristic times, the formation time of the horizon and of the singularity. We investigate the threshold of the PBH formation by taking account of the speed of light propagating between the central singularity and the surface of a perturbation to be trapped.
We report our analysis implies density perturbations with larger inhomogeneity would easily lead PBHs.
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