In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon. In a black hole, the singularity is completely enclosed by a boundary known as the event horizon, inside which the gravitational force of the singularity is so strong that light cannot escape. Hence, objects inside the event horizon—including the singularity itself—cannot be directly observed. A naked singularity, by contrast, would be observable from the outside.

Source : Wikipedia

The existence (or not) of naked singularities has not been proved or disproved - either by experimental investigations, cosmological observations, or by theoretical calculations.

The 'weak cosmic censorship hypotheses' and the 'strong cosmic censorship hypotheses' are two mathematical conjectures (from the 1960s) by Roger Penrose which suggest that such singularities can't exist. Other researchers (notably the late Stephen Hawking) maintain that they can.

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Also see : Gravitational singularitiesplugin-autotooltip__plain plugin-autotooltip_bigGravitational singularities

"A gravitational singularity, spacetime singularity or simply singularity is a location in spacetime where the mass and gravitational field of a celestial body is predicted to become infinite by general relativity in a way that does not depend on the coordinate system.