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

TL;DR

This paper analyzes the magnetosphere of Kerr-Sen black holes within EMDA theory, revealing how the dilaton parameter affects energy extraction and radiative efficiency, and compares observational data to Kerr black hole models.

Contribution

It provides a perturbative solution to the Grad-Shafranov equation for Kerr-Sen black holes and assesses the impact of the dilaton parameter on energy extraction and observational fits.

Findings

Energy extraction power increases with dilaton parameter r_2.

Radiative efficiency exceeds that of Kerr black holes.

Kerr black holes better fit observational data for certain Lorentz factors.

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 $\chi^2$ 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 $\Gamma = 2$ and $5$.