Thermodynamics of black string from Rényi entropy in de Rham–Gabadadze–Tolley massive gravity theory

Abstract The de Rham–Gabadadze–Tolley black string solution is a cylindrically symmetric and static of the Einstein field equation with graviton mass term. For asymptotically Sitter solution, it possible to obtain two event horizons corresponding thermodynamic systems. Rényi entropy one entropic forms which suitable deal nonextensive properties string. In this work, we investigated possibility stable by using in both separated effective approaches. We found that nonextensivity provides thermodynamically moderate size transition from hot gas phase moderate-sized separated/effective description first-order/zeroth-order transition. significant ways distinguish approaches are discussed.