Fuzzy spaces topology change and BH thermodynamics

Abstract

What is the ultimate fate of something that falls into a black hole? From this question arises one of the most intricate problems of modern theoretical physics: the black hole information loss paradox. Bekenstein and Hawking have been shown that the entropy in a black hole is proportional to the surface area of its event horizon, which should be quantized in a multiple of the Planck area. This led G.’t Hooft and L. Susskind to propose the holographic principle which states that all the information inside the black hole can be stored on its event horizon. From this results, one may think if the solution to the information paradox could lies in the quantum properties of the black hole horizon. One way to quantize the event horizon is to see it as a fuzzy sphere, which posses a closed relation with Hopf algebras. This relation makes possible a topology change process where a fuzzy sphere splits in two others. In this work it will be shown that, if one quantize the black hole event horizon as a fuzzy sphere taking into account its quantum symmetry properties, a topology change process to black holes can be defined without break unitarity or locality, and we can obtain a possible solution to the information paradox. Moreover, we show that this model can explain the origin of the black hole entropy, and why black holes obey a generalized second law of thermodynamics.