We will analyze a black string in dRGT massive theory of gravity. Considering different approaches, we will study the critical behavior, phase transition and thermal stability for such a black string solution. We will analyze the Van der Waals behavior for this system, and observe that the Van der Waals behavior depends on mass of graviton. We will also analyze the geometrical thermodynamics of black strings using different thermodynamic metrics. It will be observed that the thermal fluctuations can modify the behavior of this system. We will explicitly analyze the effects of such fluctuations on the stability of this black string solutions. This will be done using the Hessian matrix for this system.

我们将分析dRGT大规模引力理论中的黑线。考虑不同的方法，我们将研究这种黑弦解决方案的临界行为，相变和热稳定性。我们将分析该系统的范德华行为，并观察范德华行为取决于引力子的质量。我们还将使用不同的热力学指标分析黑弦的几何热力学。将观察到，热波动会改变该系统的性能。我们将明确分析这种波动对这种黑弦解决方案稳定性的影响。对于该系统，将使用Hessian矩阵完成此操作。