Energy Formula, Surface geometry and Energy Extraction for Kerr-Sen Black Hole

Abstract

We evaluate the \emph{surface energy~(${\mathcal{E}}_s^{\pm }$), rotational energy~(${\mathcal{E}}_r^{\pm }$) and electromagnetic energy~(${\mathcal{E}}_{em}^{\pm }$)} for a \emph{Kerr-Sen black hole~(BH)} having the event horizon~(${\mathcal{H}}^{+}$) and the Cauchy horizon~(${\mathcal{H}}^{-}$). Interestingly, we find that the \emph{sum of these three energies is equal to the mass parameter i.e. ${\mathcal{E}}_s^{\pm }+{\mathcal{E}}_r^{\pm }+{\mathcal{E}}_{em}^{\pm }=\mathcal{M}$}. Moreover in terms of the \emph{ scale parameter ~$({\zeta }_{\pm })$, the distortion parameter~(${\xi }_{\pm }$) and a new parameter~$({\sigma }_{\pm })$} which corresponds to the area~(${\mathcal{A}}_{\pm }$), the angular momentum ~$(J)$ and the charge parameter~($Q$), we find that the \emph{mass parameter in a compact form} ${\mathcal{E}}_s^{\pm }+{\mathcal{E}}_r^{\pm }+{\mathcal{E}}_{em}^{\pm }=\mathcal{M}=\frac{{\zeta }_{\pm }}{2}\sqrt{\frac{1+2{\sigma }_{\pm }^2}{1-{\xi }_{\pm }^2}}$ %\begin{eqnarray} %{\cal E}_{s}^{\pm}+{\cal E}_{r}^{\pm}+{\cal E}_{em}^{\pm}={\cal M} =\frac{ζ_{\pm} }{2} %\sqrt{\frac{1+2\,σ_{\pm}^2}{1-ξ_{\pm}^2}} \nonumber %\end{eqnarray} which is valid {through all the horizons} (${\mathcal{H}}^{\pm }$). We also compute the \emph{equatorial circumference and polar circumference} which is a gross measure of the BH surface deformation. It is shown that when the spinning rate of the BH increases, the \emph{equatorial circumference increases} while the \emph{polar circumference decreases}. Furthermore, we compute the exact expression of \emph{rotational energy that should be extracted from the BH via the Penrose process}. The maximum value of rotational energy which is extractable should occur for \emph{extremal Kerr-Sen BH} i.e. ${\mathcal{E}}_r^{+}$.

Published in GRG

References in corpus (1)

• Energy Formula for Newman-Unti-Tamburino class of Black Holes