Black string surrounded by a static anisotropic quintessence fluid

TL;DR

This paper derives an exact rotating black string solution in anti-de Sitter spacetime surrounded by quintessence matter, analyzing its properties and thermodynamics, and extends previous solutions by including background matter effects.

Contribution

It introduces a new rotating black string solution with quintessence matter in AdS spacetime, generalizing earlier models and analyzing its thermodynamic behavior.

Findings

The solution includes an additional parameter due to quintessence matter.

Thermodynamic quantities are corrected by the presence of quintessence.

The first law of thermodynamics is verified for the new solution.

Abstract

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.