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. A lot of effort has been made to understand the aspects of spacetime on the quantum scale. Among several possibilities, the approach which includes noncommutativity of spacetime proves to be promising. In this paper, we use the Hamilton–Jacobi method to study the thermodynamic properties of cylindrical black holes (black strings) in noncommutative spacetime. The behavior of the black string is also investigated 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 an 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.

黑洞多年来一直是研究的主题，不仅因为它们具有有趣的物理特性，而且因为它们似乎是研究量子尺度引力的合适工具。人们已经付出了很多努力来理解量子尺度上时空的各个方面。在几种可能性中，包括时空非交换性的方法被证明是有前途的。在本文中，我们使用 Hamilton–Jacobi 方法研究了非对易时空中圆柱形黑洞（黑弦）的热力学性质。还研究了存在反反应时黑弦的行为及其对系统的影响，可以将其理解为异常。