The Universal Coefficient Theorem and Black Holes

Abstract

General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

Universal Coefficient Theorem and Quantum Field Theory

“…It is extremely important to notice this mainly because the most natural conclusion then, is that the information related to certain objects (even physical objects) is not always encoded exclusively in their internal structure but also in the way in which they can be mapped into other objects or in the way they relate with the framework where they are being analyzed. This idea became part of my work on the missing information in black holes thermodynamics [53]. In order to continue this discussion let me define the products of objects from a categorial perspective.…”

“…When we speak about short exact sequences we also have the first map being an injection and the second a surjection. I used this property for example in [54] and it is of major importance in [53] as well. Hence, preserving exactness when we apply functors is crucial.…”