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We investigate a curvature singularity appearing in the star collapse process in F(R) gravity. In particular, we propose an understanding of the mechanism to produce the curvature singularity. Moreover, we explicitly demonstrate that Rα (1<α⩽2) term addition could cure the curvature singularity and viable F(R) gravity models could become free of such a singularity. Furthermore, we discuss the realization...
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