Energy Extraction and Particle Acceleration in String-Inspired Rotating Einstein-Maxwell-Dilaton-Axion Black Hole

Abstract

We study energy extraction and particle acceleration in the rotating Einstein-Maxwell-Dilaton-Axion (EMDA) black hole, focusing on the impact of dilaton hair $b\le 0$ on near-horizon energetics relative to Kerr. For the Penrose process we derive analytic expressions for the maximum efficiency and show that negative $b$ can strongly enhance the ideal gain in the extremal regime (e.g., reaching $\sim 91\%$ for $b=-0.3$). We then compute the irreducible mass $M_{\rm irr}$ and the corresponding rotationally extractable energy $\mathcal{E}_{\rm rot}\equiv M-M_{\rm irr}$, finding that $M_{\rm irr}$ decreases monotonically as $b$ becomes more negative while $\mathcal{E}_{\rm rot}$ increases, indicating a larger spin-energy reservoir; at extremality the extracted share from rotation is $\mathcal{E}_{\rm rot}/M\simeq 0.63$ for EMDA, reducing to the Kerr value $\simeq 0.29$ at $b=0$. Kinematic constraints relevant to fragment production are quantified via the Wald and Bardeen--Press--Teukolsky bounds, which are progressively relaxed for more negative $b$. For wave superradiance we obtain the flux balance and the amplification window $0<β<kΩ_H$, with $Ω_H$ expressed through $Ξ=r_H^{2}+2br_H+a^{2}$; negative $b$ modifies $Ω_H$ and enlarges the parameter region exhibiting negative horizon flux. Finally, we analyse two-particle collisions and derive $E_{\rm cm}$, showing that the Bañados--Silk--West divergence persists at the horizon when one particle is tuned to the critical angular momentum $L_c=E/Ω_H$, while $E_{\rm cm}$ remains finite for generic angular momenta. Overall, dilaton hair in EMDA simultaneously amplifies energy-extraction channels and reshapes the near-horizon thresholds governing high-energy collisions.

Figures (12)

• Figure 1: Panel (a) The allowed range space of the parameters $b$ for the positive values of $r$. Panel (b) The range space of the parameters $a$ and $b$ describing a black hole and a naked singularity.
• Figure 2: The efficiency of the Penrose process as a function of the parameters $b$ and $a$ is shown. The left panel displays the density (contour) distribution of $\eta_{\max}$ in the $(b,a)$ plane, while the right panel shows $\eta_{\max}$ versus $a$ for different values of $b$.
• Figure 3: The behaviour of $\Omega_H$ versus $a$ for different values of $b$.
• Figure 4: Superradiant flux profiles $P(\beta)$ versus $\beta$ for EMDA black holes in four representative configurations: (A) $a=0.6$, $b=-0.2$, $r_H=1.329$; (B) $a=0.4$, $b=-0.4$, $r_H=1.047$; (C) $a=0.8$, $b=-0.1$, $r_H=1.312$; and (D) at extremality with $a_E=0.7$, $b=-0.3$, $r_E=0.7$. In each plot, the shaded region denotes the superradiant window $0<\beta<k\Omega_H$, the dashed line marks the cutoff at $\beta=k\Omega_H$, and the minimum corresponds to $\beta_{\min}=\Omega_H$.
• Figure 5: Illustration of the radial velocity $\dot{r}$ versus the radial coordinate $r$ for an extremal EMDA black hole for different values of angular momentum $L$, $b$ and $a$. The black dotted lines correspond to $L > L_c$, the solid red line denotes $L = L_c$, and the blue dotted lines indicate $L < L_c$. The vertical dashed line denotes the location of the extremal event horizon $r_E$ of the EMDA black hole.