Penrose Process Efficiency and Irreducible Mass in Rotating Einstein-Born-Infeld Black Holes with Nonlinear Electrodynamics

TL;DR

The paper investigates rotational energy extraction from rotating Einstein--Born--Infeld black holes by incorporating nonlinear electrodynamics via a radius-dependent charge $Q_{ ext{eff}}(r)$ and the BI parameter $β$. It derives equatorial geodesics, analyzes negative-energy states with the Wald inequality, and provides a closed-form expression for the maximal Penrose efficiency $η_{ ext{max}}^{ ext{EBI}}$ that reduces to Kerr--Newman in the linear limit $β→∞$. The results show that increasing charge $Q$ or nonlinear effects generally shrink horizons and ergoregions, lowering extraction efficiency relative to Kerr and Kerr–Newman, though certain parameter ranges can exceed Kerr–Newman efficiency; nonlinear dynamics also decrease the horizon area and the irreducible mass, linking to entropy. Together, these findings connect nonlinear gauge field dynamics to black hole energetics and thermodynamics, with potential implications for high-field astrophysical environments and observable signatures of EBI spacetimes.

Abstract

We investigate the extraction of rotational energy from rotating Einstein-Born-Infeld (EBI) black holes, where nonlinear electrodynamics introduces a radius-dependent effective charge modifying the spacetime geometry. Focusing on neutral test particles in the equatorial plane, we derive analytic expressions for their kinematics and establish conditions for negative energy orbits essential to the Penrose process using the near-horizon limit and Wald inequality. We present a closed-form expression for maximal energy extraction efficiency as a function of spin, charge, and the Born-Infeld parameter $β$. Our numerical survey reveals that increasing charge and nonlinear Born-Infeld effects generally reduce horizon radius and ergoregion size, suppressing energy extraction efficiency compared to Kerr and often Kerr-Newman black holes. However, at certain spins and \$beta$, the EBI geometry can enhance efficiency beyond Kerr-Newman. We also compute the irreducible mass, showing how nonlinear electromagnetic dynamics reduce the horizon area and the associated entropy proxy. These results provide a unified picture linking nonlinear electrodynamics, horizon structure, and energy extraction efficiency across relevant parameters.

Figures (7)

• Figure 1: Parameter space of rotating EBI black holes showing spin $a$ versus charge $Q$ (left) and spin $a$ versus Born--Infeld parameter $\beta$ (right).
• Figure 2: Event (solid) and Cauchy (dotted) horizon radii versus spin $a$ for varying $Q$ (left) and $\beta$ (right).
• Figure 3: Metric function $\Delta(r)$ versus radial coordinate $r$ for rotating EBI black holes.
• Figure 4: Cross-sectional views of the ergoregion, event horizon, and static limit for various and $\beta$ and $Q$.
• Figure 5: Dependence of angular velocity $\Omega$ on $Q$ and $\beta$ versus radial distance $r$.