Black string in massive gravity

Abstract 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.