Termodinâmica de um buraco negro BTZ com um comprimento mínimo.

Abstract

The metric obtained by Ba˜nados-Teitelboim-Zanelli (BTZ) was discovered seeing the three-dimensional equivalence between gravitation and the Chern-Simons theory, a topological three-dimensional theory along with the Seiberg-Witter mapping, in which its solution is described in (2 + 1) -dimensions and its solution works with negative cosmological constant, an important field of investigation. In this work, we will consider the minimum radius of a surface density obtained from the hydrogen atom to analyze certain thermodynamic properties, such as Hawking temperature, entropy and heat capacity, comparing our results with those related to a non-commutative BTZ hole, so we can see if such effects are valid in this type of mass distribution or if they violate the thermodynamics laws. The geodesic structure of the BTZ minimum length black holes for massless and massive particles is discussed as well.