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. Moreover, the dRGT black string solution includes 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. 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.
Highlights
Adding generic mass terms for the graviton on given background usually brings about various instabilities and ghosts for the gravitational theories
There have been plenty interesting approaches to tackle the complexity to obtain spherical symmetric solutions in massive gravity theories [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. It was found by Vegh [4] that a spherically symmetric black hole with a Ricci flat horizon is a solution to the four-dimensional massive gravity and the solution was studied in the aspect of thermodynamical properties and phase transition structure [5,6]
We have presented a class of black strings, both charged and uncharged, in dRGT massive gravity where the effective cosmological constant is negative, and we studied the thermodynamics and phase structure of the solutions in both the grand canonical and the canonical ensembles
Summary
Adding generic mass terms for the graviton on given background usually brings about various instabilities and ghosts for the gravitational theories. The allowed interaction terms for the four-dimensional theory consist of three kinds of combination; the quadratic, the cubic, and the quartic orders of the metric Such nonlinearities involve complexities in the calculation as a price to pay for eliminating the ghost and usually make it cumbersome to find an exact solution. Lemos [38] has shown a possibility of cylindrical black holes from the gravitational collapse with cylindrical matter distribution in an anti-de Sitter spacetime, violating in this way the hoop conjecture. This cylindrically static black hole solutions in an anti-de Sitter spacetime are called black strings. We will find the solution to this equation of motion by imposing the static and axial symmetry
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