Correção não-comutativa para a termodinâmica do buraco negro BTZ.

Abstract

The theory of general relativity predicts that a sufficiently compact mass can deform space-time to form a black hole. The boundary of the region from which it is not possible to escape is called the event horizon. The metric obtained by Bañados-Teitelboim-Zanelli (BTZ) was found considering the equivalence in three dimensions between gravitation and the Chern-Simons theory, a topological theory in three dimensions, with the Seiberg-Witter mapping, in which its solution is described in (2 + 1) -dimensions and their solution it works with negative cosmological constant, an important field of investigation in which it takes into account the possibility of modifying Heisenberg’s Uncertainty Principle, which introduced a fundamental length scale. Thus, this modification generates corrections in the thermodynamic properties of black holes. In this work we take into account the principle of generalized uncertainty (GUP) in the tunneling formalism via the Hamilton-Jacobi method, to determine the Hawking temperature and entropy of non-commutative BTZ black holes. From this approach we were able to achieve several correction results, including the expected logarithmic correction for the area entropy associated with non-commutative BTZ black holes. We also addressed the question of the stability of the non-commutative BTZ black hole, investigating its specific modified heat capacity.