As is common knowledge, gravitationally collapsing objects of sufficient mass are doomed to form black holes (BHs), defined by an event horizon within which resides the singularity of the general relativistic equations. All information about the initial state of the object is radiated away during the collapse and, remarkably, the general stationary solution depends on only three externally observable parameters: mass M, angular momentum J, and charge Q of the BH. This scenario is encapsulated in John Wheeler's phrase that ``A black hole has no hair."
Building upon a general proof by Stephen Hawking that the BH surface area cannot decrease in any process (Ref.100), Jacob Bekenstein recognized the similarity to the mandated increase of entropy in thermodynamics, and thence the relation to Shannon's information measure (Ref.101). A BH can be created in a number of ways, leading to a number of possible internal configurations corresponding to the same set of external parameters. One then defines the BH entropy as a measure of the inaccessibility of this information. Note carefully that this entropy refers to an equivalence class of BHs, and has nothing to do with thermal entropy inside the BH. After careful consideration Bekenstein found this entropy to be
where 
is Boltzmann's constant, G is the gravitational constant, and A is the surface area of the BH. This is an enormous number, but appropriate to the maximum entropy of a massive collapsing object.
All this is relatively straightforward and provides an interesting example of the role of information theory in general relativity. To an outside observer the original information is not missing, it simply resides inside the BH and can be described by a pure state. But in 1976 Hawking made the theoretical discovery, by means of an appropriate blending of quantum mechanics and general relativity, that BHs can radiate away their energy thermally (Ref.102). One can think of this as pair creation in the presence of a strong gravitational field, with one member going down the hole and the other moving off to infinity. Consequently, as the BH evaporates two related contradictions emerge: the final thermal state is a mixed state, in contradiction of the quantum theorem that a pure state cannot evolve to a mixed state; and, all the information encapsulated within the BH somehow is lost forever when the BH finally disappears. This is the BH information paradox.
Attempts at a resolution now constitute a very active area of research in general relativity and quantum field theory. At this time there are essentially three separate views: (1) gravitational effects introduce an additional uncertainty over and above Heisenberg's into quantum physics; (2) the Hawking radiation may not be completely thermal, but actually carries away the information; (3) it is possible that the BH does not evaporate completely and the information remains within a Planck-scale ( 
cm) remnant. These three lines of thought are explored in the references below.
Subsequently Bekenstein developed BH thermodynamics a bit further (Ref.104) by utilizing the principle of maximum entropy to verify a generalized, intrinsically quantum second law. This asserts that BH entropy plus ordinary entropy exterior to BHs never decreases. Note that this is a theoretical statement of a statistical law that goes beyond ordinary thermodynamics.
The following five papers provide the original literature connecting BHs to information theory.
A selection of articles representing current research on the information paradox follows.