# Black String in dRGT Massive Gravity

## TL;DR

This paper introduces a new black string solution in dRGT massive gravity, analyzing its thermodynamics and stability, and revealing the significant impact of graviton mass on black string properties and phase transitions.

## Contribution

It presents the first cylindrically symmetric black string solution in dRGT massive gravity, including charged and uncharged cases, and explores their thermodynamic behavior and phase transitions.

## Key findings

- Graviton mass significantly alters black string thermodynamics.
- Hawking-Page phase transition occurs for dRGT black strings.
- Black string stability depends on radius, with a critical point for stability.

## Abstract

We present a cylindrically symmetric solution, both charged and uncharged, which is known as a black string solution to the nonlinear ghost-free massive gravity found by de Rham, Gabadadze, and Tolley (dRGT). This "dRGT black string" can be thought of as a generalization of the black string solution found by Lemos \cite{1}. Moreover, the dRGT black string solution also include other classes of black string solution such as the monopole-black string ones since the graviton mass contributes to the global monopole term as well as the cosmological constant term. To investigate the solution, we compute mass, temperature, and entropy of the dRGT black string. We found that the existence of the graviton mass drastically affects the thermodynamics of the black string. Furthermore, the Hawking-Page phase transition is found to be possible for the dRGT black string as well as the charged dRGT black string. In terms of their stability, the dRGT black string solution is thermodynamically stable for $r>r_c$ with negative thermodynamical potential and positive heat capacity while it is unstable for $r<r_c$ where the potential is positive.