on the no-hair theorem to arrive at the conclusion that radiation emitted by black holes would depend only on a few macroscopic parameters such as the black hole's mass, charge and spin and not on the details of the initial state that led to the formation of the black hole. Moreover, the argument for information loss relied on the causal structure of the black-hole spacetime, which suggests that information in the interior should not affect any observation in the exterior including observations performed on the radiation emitted by the black hole. If so, the region of spacetime outside the black hole would lose information about the state of the interior after black-hole evaporation leading to the loss of information. Today, some physicists believe that the holographic principle (specifically the AdS/CFT duality) demonstrates that Hawking's conclusion was incorrect, and that information is in fact preserved. Black hole evaporation In 1973–1975, Stephen Hawking showed that black holes should slowly radiate away energy and Hawking later argued that this leads to a contradiction with unitarity. Hawking used the classical no-hair theorem to argue that the form of this radiation – called Hawking radiation – would be completely independent of the initial state of the star or matter that collapsed to form the black hole. Hawking argued that the process of radiation would continue until the black hole had evaporated completely. At the end of this process, all the initial energy in the black hole would have been transferred to the radiation. But, according to Hawking's argument, the radiation would retain no information about the initial state and therefore information about the initial state would be lost. More specifically, Hawking argued that the pattern of radiation emitted from the black hole would be random, with a probability distribution controlled only by the initial temperature, charge and angular momentum of the black hole and not by the initial state of the collapse. The state produced by such a probabilistic process is called a mixed state in quantum mechanics. Therefore, Hawking argued that if the star or material that collapsed to form the black hole started in a specific pure quantum state, the process of evaporation would transform the pure state into a mixed state. This is inconsistent with the unitarity of quantum-mechanical evolution discussed above. The loss of information can be quantified in terms of the change in the fine-grained von Neumann entropy of the