Stephen Hawking denies his own theory about information falling into black holes: the information they emit in the form of radiation contains traces of the information that fell into them. In fact, the particle-antiparticle pair that forms in the event horizon separates, and one falls in while the other forms Hawking radiation. As the first particle falls, it interacts with the matter already in it, making a “measurement” that is “teleported” to the other particle outside (a phenomenon called entanglement), which then carries information from the matter inside outward, reprocessing it (somehow).
