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In the early 90s, John Preskill, Sidney Coleman, Frank Wilzcek and Lawrence Krauss presented a series of papers [1][2][3] on Quantum Hair on Black Holes due to Cosmic strings in a number of ways involving for example the Aharonov-Bohm effect.

On the other hand in the famous posthumous Hawking, and Storminger paper [4], the notion of soft hair is presented which seems to be a more intrinsic kind of quantum hair due to quantum fluctuations in the Black Hole's event horizon. The reasoning for this soft hair stemming from a conservation argument.

What's the difference, if there is any, between the quantum hair mentioned in the two selections of literature?

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