Kiselev black strings: the charged rotating solutions

TL;DR

This work derives an exact charged rotating black string in AdS spacetime surrounded by a Kiselev anisotropic fluid by solving the Einstein–Maxwell equations with a negative cosmological constant $\\Lambda = -3/l^{2}$. The static solution is extended to rotation via a coordinate transformation, yielding a metric with horizon structure governed by the equation of state parameter $w_q$ and quintessence density $N_q$, as well as charge $Q$. Conserved charges (mass, angular momentum, electric charge) are computed with the Brown–York formalism, and the first law of thermodynamics is established. The authors obtain the Hawking temperature from scalar-field tunneling and analyze entropy and heat capacity to study thermodynamic stability, showing how quintessence and charge modify horizon properties, radiation, and phase structure; the Lemos black string is recovered in appropriate limits.

Abstract

We investigate the properties of a charged rotating black string immersed in a Kiselev anisotropic fluid in anti-de Sitter (AdS) spacetime. The Einstein-Maxwell equations with an anisotropic stress-energy tensor and cosmological constant are analyzed and solved exactly. In this work, we calculate the Kretschmann scalar, obtaining a consistent result that agrees with the existing literature in the absence of charge and fluid. The rotating solution is obtained by applying a coordinate transformation on time and angular coordinates. The event horizon associated with specific values of the equation of state parameter $w_q$ is studied. The results show an important influence of the fluid parameters $N_{q}$ and $w_{q}$, the charge parameter $Q$, and the rotation parameter $a$ on the size of the black string horizon. In addition, we determine the conditions for the existence of closed timelike curves (CTCs) and compute the conserved charges, such as mass, angular momentum, and electric charge of the black string. Utilizing the Klein-Gordon equation, we employ the quantum particle tunneling approach to obtain the probability of charged scalar particles tunneling across the event horizon. We obtain the correspondent Hawking temperature as a consequence. Furthermore, we examine the thermodynamic properties, including entropy and heat capacity, to assess the effects of the quintessence field and charge on the black string. The results include particular cases such as the Lemos black string, providing a broader view of black string configurations in AdS spacetime.

Figures (14)

• Figure 1: Plot of the event horizon with respect to the radial variable $r$ and the parameter $m$ with $Q=1$ and $N_q=-1$. $N_{q}$ is given in units of $l^{3w_{q}+1}$ and $r$ in units of $l$
• Figure 2: Plot of the event horizon with respect to the radial variable $r$ and the parameter $Q$ with $m=1$ and $N_q=-1$.
• Figure 3: Plot of the event horizon with respect to the radial variable $r$ and the parameter $N_q$ with $m=1$ and $Q=1$.
• Figure 4: Plot of the event horizon with respect to the radial variable $r$. With $Q=0.4$ and $N_q=-0.4$.
• Figure 5: Plot of the event horizon with respect to the radial variable $r$. With $m=0.4$ and $N_q=-0.4$.