Universal thermodynamic topological classes of the charged dRGT black string

Abstract

In this study, we explore universal thermodynamic topological classes of charged dRGT black string within both the canonical ensemble and grand canonical ensemble frameworks, and further analyze its asymptotic behavior under limiting parameter regimes. We demonstrate that, while the outermost large black string branch remains thermodynamically stable in both ensembles, the innermost small black string branch exhibits distinctly different stability properties: it is stable in the canonical ensemble but becomes thermodynamically unstable in the grand canonical ensemble, corresponding to the $W^{1+}$ and $W^{0-}$ topological categories, respectively. Furthermore, the local thermodynamic stability of the charged dRGT black string is investigated through the behavior of the heat capacity. These findings demonstrate that the selection of thermodynamic ensemble has a significant influence on the thermodynamic configuration of the charged dRGT black string. In the limit where gravitational effects are neglected, the charge contribution does not modify the underlying topological classification. This implies that the coupling between dRGT massive gravity and the electromagnetic sector is essential for the emergence of nontrivial thermodynamic topology. These results contribute to a deeper understanding of the black string thermodynamics and provide a novel theoretical basis for exploring the basic properties of quantum gravity.