Ergosphere Dynamics and Rotational Energy Extraction in Bumblebee Kerr-Newman-AdS Black Holes

TL;DR

The paper investigates Bumblebee Kerr-Newman-AdS black holes, introducing Lorentz-violating effects through a vector field parameter $l$ and examining their influence on horizon structure, thermodynamics, Hawking-radiation sparsity, photon geodesics, shadows, ergosphere geometry, and Penrose energy extraction. It derives analytic expressions for the horizon radii via $oldsymbol{ackslashDelta_r}$, computes $T_H$, $S$, and $C_V$ to reveal remnant formation and extended stability, and shows that Lorentz violation enhances the sparsity of emission and broadens the ergoregion, thereby increasing extraction efficiency through the Penrose process. Photon trajectories are analyzed with Hamilton–Jacobi methods, yielding shadow observables that depend on $l$, $a$, $Q$, and $oldsymbol{ackslashLambda}$, providing a direct link to EHT observations. The results collectively demonstrate that even modest Lorentz-violating effects imprint measurable changes in horizon geometry, radiation spectra, and energy-extraction processes, offering a concrete framework to test Lorentz symmetry breaking in strong gravitational fields. The work suggests observational constraints and future directions, including quasinormal modes, accretion-disk emissions, gravitational-wave echoes, and holographic connections in AdS/CFT contexts.

Abstract

We present a comprehensive analysis of the thermodynamic and optical properties of the Bumblebee Kerr-Newman-Anti-de Sitter (AdS) black hole, a rotating and charged configuration arising in Lorentz symmetry-violating (LSV) gravity. The influence of the black hole parameters on the horizon structure, thermodynamic stability, and geometric deformation of spacetime is systematically investigated. Explicit expressions for the Hawking temperature, entropy, and heat capacity are derived, revealing the formation of black hole remnants and extended stability phases induced by Lorentz symmetry-violating (LSV) effects. The sparsity of Hawking radiation is quantified, showing that Lorentz violation suppresses the continuum limit and produces a more discrete, less thermal emission spectrum. A detailed analysis of null geodesics is performed to determine the photon region and shadow morphology, indicating that increasing l and Q compresses and distorts the shadow boundary, while rotation diminishes its overall size. The ergosphere geometry is analyzed in detail, showing that increases in a, l, and Q not only enlarge and distort the ergoregion but also intensify frame-dragging, thereby maximizing the efficiency of energy extraction via the Penrose process. These results reveal clear and potentially observable deviations from standard Kerr-Newman-AdS predictions, providing a powerful new avenue to probe Lorentz symmetry breaking and test the fundamental structure of gravity in extreme strong field regimes.

Figures (14)

• Figure 1: Plot of $\Delta_r$ versus $r$ for different values of the black hole parameters, illustrating the effects of (a) Lorentz-violating parameter $l$, (b) rotation parameter $a$, and (c) electric charge $Q$.
• Figure 2: Event horizon ($r_+$, thick line) and Cauchy horizon ($r_-$, dashed line) as functions of the rotation parameter $a$ for different values of (a) $l$, (b) $\Lambda$, and (c) $Q$. The plots show how Lorentz-violating effects, cosmological curvature, and charge modify the horizon structure.
• Figure 3: Hawking temperature $T_H$ versus horizon radius $r_h$ for different black hole parameters: (a) varying $l$, (b) varying $\Lambda$, (c) varying $a$, (d) varying $Q$. Extremal points shift with rotation, charge, and Lorentz-violating parameters, defining critical radii for evaporation and remnant formation.
• Figure 4: Entropy $S$ versus rotation parameter $a$ for varying parameters: (a) $l$, (b) $\Lambda$, (c) $Q$. The decreasing trend with $a$ correlates with shrinking horizon area, while parameter variations shift the entropy curves, revealing effects of Lorentz violation, cosmological constant, and the charge.
• Figure 5: Heat capacity $C_V$ versus horizon radius $r_h$ for varying parameters: (a) $l$, (b) $\Lambda$, (c) $a$, (d) $Q$. Positive values correspond to stable phases, negative values to instability, with divergences defining critical radii of phase transitions influenced by rotation, charge, and Lorentz-violating effects.