The information paradox: A pedagogical introduction

The black hole information paradox tells us something important about the way quantum mechanics and gravity fit together. In these lectures I try to give a pedagogical review of the essential physics leading to the paradox, using mostly pictures. Hawking's argument is recast as a `theorem': if quantum gravity effects are confined to within a given length scale and the vacuum is assumed to be unique, then there will be information loss. We conclude with a brief summary of how ...

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importa...

I distinguish between two versions of the black hole information-loss paradox. The first arises from apparent failure of unitarity on the spacetime of a completely evaporating black hole, which appears to be non-globally-hyperbolic; this is the most commonly discussed version of the paradox in the foundational and semipopular literature, and the case for calling it `paradoxical' is less than compelling. But the second arises from a clash between a fully-statistical-mechanical...

The black-hole information paradox has fueled a fascinating effort to reconcile the predictions of general relativity and those of quantum mechanics. Gravitational considerations teach us that black holes must trap everything that falls into them. Quantum mechanically the mass of a black hole leaks away as featureless (Hawking) radiation, but if the black hole vanishes, where is the information about the matter that made it? We treat the states of the in-fallen matter quantum...

We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a refinement of the paradox that makes essential reference to the black-hole interior. This analysis leads to a broadly-applicable physical principle: in a theory of quantum gravity, a copy of all the information on a Cauchy slice is also available ...

The black hole information paradox arises from an apparent conflict between the Hawking black hole radiation and the fact that time evolution in quantum mechanics is unitary. The trouble is that while the former suggests that information of a system falling into a black hole disappears, the latter implies that information must be conserved. In this work we discuss the current divergence in views regarding the paradox, we evaluate the role that objective collapse theories coul...

The information paradox in the quantum evolution of black holes is studied within the framework of the AdS/CFT correspondence. The unitarity of the CFT strongly suggests that all information about an initial state that forms a black hole is returned in the Hawking radiation. The CFT dynamics implies an information retention time of order the black hole lifetime. This fact determines many qualitative properties of the non-local effects that must show up in a semi-classical eff...

We resolve black hole information paradox within semiclassical gravity, in a manner that does not depend on details of unknown quantum gravity. Our crucial insight is that outgoing Hawking particles are physical only far from the black hole horizon, so they are created far from the horizon and entangled with degrees of freedom closer to the horizon. The latter degrees of freedom can be understood as quasi-classical coherent states, implying that Hawking radiation is accompani...

This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given ...

The vivid debate concerning the paradox of information being lost when objects are swallowed by a black hole is shown to be void. We argue that no information is ever missing for any observer neither located above, nor falling beneath the event horizon. The information is preserved in a classical scenario of eternal black holes and semi-classical one allowing Hawking radiation.