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In general relativity, a naked singularity is a gravitational singularity, without an event horizon. In a black hole, there is a region around the singularity, the event horizon, where the gravitational force of the singularity is strong enough so that light cannot escape. Hence, the singularity cannot be directly observed. A naked singularity, by contrast, is observable from the outside.
The theoretical existence of naked singularities is important because their existence would mean that it would be possible to observe the collapse of an object to infinite density. It would also cause foundational problems for general relativity, because in the presence of a naked singularity, general relativity cannot make predictions about the future evolution of spacetime.
Some research has suggested that if loop quantum gravity is correct, then naked singularities could exist in nature, implying that the cosmic censorship hypothesis does not hold. Numerical calculations and some other arguments have also hinted at this possibility.
To this date, no naked singularities (and no event horizons) have been observed.
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