Rotating Kiselev Black Holes in $f(R,T)$ Gravity

TL;DR

This paper constructs rotating black hole solutions in $f(R,T)$ gravity starting from spherical Kiselev black holes, revealing complex horizon structures and dependencies on parameters, which can test modified gravity theories against astrophysical observations.

Contribution

It introduces a novel method to generate rotating Kiselev black holes in $f(R,T)$ gravity using a modified Newman-Janis algorithm, expanding the class of exact solutions in modified gravity theories.

Findings

Existence of critical values of parameters for extremal black holes.

Diverse horizon structures depending on parameters $a$, $eta$, and $w$.

Rich spacetime structures influenced by $f(R,T)$ gravity effects.

Abstract

Exact solutions describing rotating black holes can provide significant opportunities for testing modified theories of gravity, which are motivated by the challenges posed by dark energy and dark matter. Starting with a spherical Kiselev black hole as a seed metric, we construct rotating Kiselev black holes within the $f(R,T)$ gravity framework using the revised Newman-Janis algorithm - the $f(R,T)$ gravity-motivated rotating Kiselev black holes (FRKBH), which encompasses, as exceptional cases, Kerr ($K=0$) and Kerr-Newman ($K=Q^2$) black holes. These solutions give rise to distinct classes of black holes surrounded by fluids while considering specific values of the equation-of-state parameter, $w$, for viable choices for the $f(R,T)$ function. From the parameter space or domain of existence of black holes defined by $a$ and $\gamma$ for FKRBH, we discover that when $a_1<a<a_2$, there is a critical value $\gamma=\gamma_E$ which corresponds to extreme value black holes portrayed by degenerate horizons. When $a<a_1$ ($a>a_2$), we encounter two distinct critical values $\gamma=\gamma_{E1}, \; \gamma_{E2}$ with $\gamma_{E1}>\gamma_{E2}$ (or $\gamma=\gamma_{E3},\; \gamma_{E4}$ with $\gamma_{E3}>\gamma_{E4}$. We delve into the horizon and global structure of FKRBH spacetimes and examine their dependence on parameters $w$ and $\gamma$. This exploration is motivated by the remarkable effects of $f(R,T)$ gravity, which gives rise to diverse and intricate spacetime structures within the domain where black holes exist.