CARVALHO, B. R.; http://lattes.cnpq.br/4760996445176055; CARVALHO, Bruno Rego de.
Resumo:
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.