The perturbation solutions to the Blandford-Znajek mechanism in the Kerr-Sen black hole

Abstract

We investigate the steady, axisymmetric, force-free magnetosphere of Kerr-Sen black hole (BH) within the framework of the Einstein-Maxwell-dilaton-axion (EMDA) theory. By perturbatively solving the nonlinear Grad-Shafranov (GS) equation, we determine the magnetic field configuration and quantify the influence of the dilaton parameter $r_2$ on the energy extraction rate and radiative efficiency. Our results show that both the energy extraction power and the radiative efficiency increase with $r_2$, exceeding those of the standard Kerr BH, whereas the extraction efficiency remain consistent with the Kerr case. In addition, we perform $χ^2$ statistical analysis using observational data from six binary BH systems, which indicates that the Kerr BH currently provides a better fit for bulk Lorentz factors $Γ= 2$ and $5$.

Figures (4)

• Figure 1: The horizontal axis represents the dilaton parameter $r_2$, while the vertical axis denotes the BH spin $a$. The red region corresponds to the parameter space where two distinct event horizons exist, whereas the white region indicates the domain in which naked singularity appears.
• Figure 2: The left graph illustrates the ratio of energy extraction rate for the two BHs as a function of dilaton parameter $r_2$. The right graph depicts the ratio of angular velocity for a fixed $r_2$ as a function of spin $a$.
• Figure 3: The bottom panel shows the shape of the ergoregion of the Kerr-Sen BH for $a = 0.5M$ and $0.7M$ with different values of $r_2$ in the $(r \sin\theta,\, r \cos\theta)$ plane.
• Figure 4: The graph illustrates the variation of $\chi^2$ with the dilaton parameter $r_2$ for six binary BHs. The red dashed line represents the situation when $P_{\text{jet}}$ corresponding to $\Gamma=2$ is used to calculate the $\chi^2$, while the blue dashed line is associated with the scenario when $P_{\text{jet}}$ corresponding to $\Gamma=5$ is considered for evaluating the $\chi^2$.