The occurrence of naked singularities in gravitational collapse gives rise to several most intriguing questions and cosmic puzzles. Profound issues such as the status of the cosmic censorship hypothesis ruling out naked singularities, and those related to the nature and structure of naked singularities arise. Some of these are discussed in this chapter, together with a discussion on various questions that come up about naked singularities and gravitational collapse. A major issue here is whether naked singularities are stable and generic, if they form in realistic collapse in astrophysical scenarios. The chapter discusses our recent understanding on this issue. Several most intriguing questions arise on the physics and implications of naked singularities, such as the nature of spacetime in their vicinity, causality violation if any near the same, possible energy emissions from these regions, and the quantum gravity effects near the same. these problems are discussed and debated here in this chapter.
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