Black string surrounded by a static anisotropic quintessence fluid

A black string is a solution of the four-dimensional general relativity in cylindrical symmetric anti-de Sitter (AdS) spacetime pioneered by Lemos [6]. We obtain an exact rotating black string surrounded by quintessence matter in anti-de Sitter (AdS) spacetime and analyze its properties. The solution has an additional parameter $N_q$ due to background quintessence matter and it also depends on quintessence state parameter $w_q$. Our rotating solution encompasses the Lemos black string \cite{Lemos:1994xp}, which can be recovered in the absence of background matter ($N_q=0$). The special case of rotating charged black string ($w_q=1/3$) has both Cauchy and event horizons. We find that thermodynamic quantities mass, temperature, entropy and heat capacity get corrected due to quintessence background. The counterterm method is utilized to calculate the associated conserved quantities to conclude that the first law of thermodynamics is satisfied. The cloud of strings background ($w_q= -1/3$) has been included as a special case.