The black hole information paradox results from the combination of quantum mechanics and general relativity.
In 1975, Stephen Hawking and Jacob Bekenstein showed that black holes should slowly radiate away energy, which poses a problem. From the no hair theorem one would expect the Hawking radiation to be completely independent of the material entering the black hole. However, if the material entering the black hole were a pure quantum state, the transformation of that state into the mixed state of Hawking radiation would destroy information about the original quantum state. This violates the rules of quantum mechanics and presents a seeming physical paradox.
In 1997 John Preskill bet Hawking and Kip Thorne that information was not lost in black holes.
In July 2004 Stephen Hawking announced a theory that quantum perturbations of the event horizon could allow information to escape from a black hole, which would resolve the information paradox. However, as of 2004 the full details of the theory have yet to be published, so most peers are reserving judgement before accepting the result.
When announcing his result Hawking also conceded the 1997 bet, paying Preskill with a baseball encyclopedia (ISBN 189496327X) 'from which information can be retrieved at will'.
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