Black String Thermodynamics in Noncommutative Spacetime: Anomaly and Phase Transition

Black holes have been a subject of investigation over years not only because they have interesting physical properties, but also because they seem to be the appropriate tool for studying gravity in quantum scale. Although a lot of effort has been made to understand the aspects of spacetime on the quantum scale, the approach which includes noncommutativity of spacetime proves to be promising among several possibilities. In this paper, we use the Hamilton-Jacobi method to study the thermodynamic properties of cylindrical black holes (black strings) in noncommutative spacetime. It is also investigated the behavior of the black string in the presence of back reaction as well as its influence on the system can be understood as an anomaly. This work aims to provide understanding about black strings thermodynamics in noncommutative spacetime since this scale of spacetime is important for the comprehension of the relation between quantum mechanics and general relativity.