Kiselev black strings in $f(R,T)$ gravity

Abstract

In this work, we investigate exact black string solutions in the context of $f(R,T)$ gravity. Adopting the specific form $f(R,T) = R + 2χT$, we consider an anisotropic Kiselev fluid as the matter content and obtain static cylindrical solutions, which are then extended to the rotating case through a suitable coordinate transformation. The influence of the quintessence state parameter $w_q$ and the matter--geometry coupling constant $χ$ on the geometry is analyzed. We examine the weak, null, and strong energy conditions, identifying the regions in the parameter space where they are satisfied. Furthermore, we apply the Hamilton--Jacobi method to study the tunneling of scalar particles across the event horizon and derive the corresponding Hawking temperature. The thermodynamic stability of the solutions is investigated by computing the heat capacity, and the conditions for phase transitions are discussed. The results provide a characterization of black strings in $f(R,T)$ gravity surrounded by quintessence, highlighting the combined effects of anisotropic matter and modified gravity on their physical properties.

Figures (3)

• Figure 1: Behavior of the metric function $F(r)$ as a function of the radial coordinate $r$. The plots are shown for fixed parameters $K = 2$, $\ell = 10$, and $M = 1$, and different values of the quintessence state parameter $w_q$ and the coupling parameter $\chi$. Each panel corresponds to a different value of $\chi$, namely $\chi = 0$, $0.2$, $0.8$, and $-0.8$. The curves represent $w_q = -1/3$ (red), $w_q = 0$ (blue), and $w_q = 1/3$ (black).
• Figure 2: Energy density $\rho(r)$ as a function of the radial coordinate $r$ for a black string configuration. The plots are shown for fixed parameters $K = 0.4$, $\ell = 40$, and $M = 1$, and different values of the quintessence state parameter $w_q$ and the coupling parameter $\chi$. Each panel corresponds to a different value of $\chi$, namely $\chi = 0$, $0.2$, $0.4$, and $-0.8$. The curves represent $w_q = -1/3$ (red), $w_q = 0$ (blue), and $w_q = 1/3$ (black).
• Figure 3: This is the plot of the region where all the energy conditions considered in this paper are satisfied, for $M=1$, $l=40$, and $K=-0.4$.