From Information To Black Holes:a Study On The Applications Of Informationtheoretic Methods In Black Hole Physics

This thesis is a study on some applications of information theory in black hole physics. The methods of information theory to be used in this thesis are relative entropy and information geometry. This thesis consists of two parts:(1) We use relative entropy to characterize the thermodynamics of quantum decoherence, and we consider Hawking radiation from a black hole as the effect of decoherence of a two-mode squeezed state in the black hole spacetime, so that we can further use the properties of relative entropy to derive the four laws of black hole thermodynamics. The advantage of this derivation is that we can understand black hole thermodynamics purely from quantum theory since the knowledge of spacetime geometry is reduced to a minimum, which is helpful in understanding the black hole analogues in laboratories.(2) We revist the reconstruction of quantum formalism from the information geometry of a probability distribution, and enhance it with more elaborate presentations. Then we apply this reconstruction to the case of evaporating black holes, and thus obtain a possible quantum mechanics of black holes. We further give possible physical interpretions to each step of this reconstruction.In paticular, we calculate the Chern number(topological charge) of the reconstructed K?hler manifold, and represent the reconstructed dynamics in terms of fuzzy spheres in noncommutative geometry. Then we study the relationship between the entanglemt entropy of the monopoles on the fuzzy sphere and the black hole entropy calculated from the various quantum gravity models, and show their consistency. Besides, we prove that the black hole horizon indeed admits the algebraic structure of a fuzzy sphere given that in the loop quantum gravity description of black holes some black hole horizon degrees of freedom satisfy anyon statistics. This construction gives a possible dynamical explaination of the asserted information conservation based on the tunneling picture.