Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

TL;DR

This paper explores a theoretical connection between black hole entropy and topological entropy within the framework of noncommutative geometry, utilizing the Baum-Connes conjecture and insights from superstring theory and M-Theory.

Contribution

It proposes a novel conceptual link between black hole thermodynamics and topological invariants in noncommutative geometry, extending the understanding of entropy in quantum gravity.

Findings

Qualitative relation between black hole and topological entropy

Application of Baum-Connes conjecture to foliated noncommutative spaces

Insights from superstring theory and M-Theory on entropy origin

Abstract

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.