Termodinâmica de uma solução do tipo Schwarzschild com uma teoria de gauge não-comutativa da gravidade

Abstract

In this work we obtain the thermodynamic quantities for a Schwarzschild black hole with a non-commutative gauge theory of gravity, obtained by Bufalo and Tureanu. We begin with a brief review of black holes in Einstein's theory of general relativity, which presents the main solutions, as well as their characteristics, of black holes found in the literature. Then, we introduced the formalism of the Quantum Field Theory in curved spacetime and discussed the Hawking effect and black hole radiation. We will show that black holes behave like thermal systems obeying the laws of thermodynamics. We discuss alternative methods of obtaining Hawking radiation, more precisely the Hamilton-Jacobi equation method and that of null geodesics, based on the vision of the Hawking effect as a tunneling process, thus being purely semi-classical methods. That done, we introduce Non-Commutative Geometry, its motivations and how to implement it in physical theories, including gravity. We discussed some attempts to obtain a noncommutative version of the Schwarzschild solution and why they fail to try to regularize the singular behavior at origin and temperature. Based on another view of the use of non-commutativity, we show the motivations that led to the complete Schwarzschild non-commutative solution determined by Nicolini and show the new characteristics that this metric brings. Finally, we will determine the Bufalo and Tureanu solution and analyze its main characteristics. We finish with the calculations of the thermodynamics of the Bufalo's solution. It is found the small corrections that non-commutativity brought to this solution, although,as we will see, no regularity is yet expected in comparison with the usual case.