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We investigate the spherically symmetric gravitational collapse of anincoherent dust cloud by considering a LTB type space-time in third orderLovelock Gravity without cosmological constant, and give three families ofLTB-like solutions which separately corresponding to hyperbolic, parabolic andelliptic. Notice that the contribution of high order curvature corrections havea profound influence on the nature of the singularity, and the global structureof space-time changes drastically from the analogous general relativistic case.Interestingly, the presence of high order Lovelock terms leads to the formationof massive, naked and time-like singularities in the 7D space-time, which isdisallowed in general relativity. Moveover, we point out that the nakedsingularities in the 7D case may be gravitational weak therefore may not be aserious threat to the cosmic censorship hypothesis, while the nakedsingularities in the $D\geq8$ inhomogeneous collapse violate the cosmiccensorship hypothesis seriously.

Spherically symmetric gravitational collapse of a dust cloud in third order Lovelock Gravity