Energy Extraction from Rotating Charged Black Holes in Kalb-Ramond Gravity

Abstract: This work presents a comprehensive study of energy extraction via the Comisso-Asenjo magnetic reconnection mechanism from rotating charged black holes in the context of Kalb-Ramond (KR) gravity. We systematically investigate the influence of various parameters on the energy extraction process, comparing the results in two distinct regions: the circular orbit region and the plunging region. {The results reveal that the Lorentz-violating parameter has a significant impact on energy extraction, affecting not only the parameter space where energy extraction is possible, but also the energy extraction power and efficiency.} It is found that the energy extraction process in the circular orbit region can offer a promising avenue for constraining KR gravity. In contrast, although energy extraction from the plunging region remains feasible even for black holes with relatively low spins and takes place nearer to the event horizon, its sensitivity to the Lorentz-violating parameter is significantly reduced. Overall, the Comisso-Asenjo magnetic reconnection mechanism can serve as a probe of the KR field, particularly through the energy extraction process in the circular orbit region.

• The paper demonstrates that introducing the KR field (characterized by parameter ℓ) significantly modifies the black hole spacetime, shifting extraction regions and critical radii.
• It employs the Hamilton-Jacobi formalism to derive particle geodesics, quantifying how spin, charge, plasma magnetization, and field orientation affect extraction power and efficiency.
• The findings imply that high-energy jet observations near the photon sphere can act as probes for Lorentz-violating effects, while the plunging region shows weaker sensitivity.

Energy Extraction from Rotating Charged Black Holes in Kalb-Ramond Gravity

Introduction and Motivation

This paper presents a detailed analysis of the Comisso-Asenjo magnetic reconnection mechanism for extracting energy from rotating charged black holes within the framework of Kalb-Ramond (KR) gravity (2602.21555). The study targets modifications introduced by the KR field, an antisymmetric tensor field native to string theory, which causes spontaneous Lorentz symmetry breaking characterized by a dimensionless parameter $\ell$. The work explores two distinct regimes — the circular orbit region and the plunging region — and rigorously investigates how parameters such as black hole spin ($a$), charge ($Q$), plasma magnetization ($\sigma$), field orientation ($\xi$), and the Lorentz-violating parameter ($\ell$) affect both the feasibility and efficiency of energy extraction.

KR gravity alters the spacetime geometry and the dynamics of astrophysical black holes by modifying standard metrics and shifting critical radii such as the event horizon, ergosphere, ISCO, and photon sphere. This study aims to quantify these modifications and highlight the potential of energy extraction processes as probes for Lorentz-violating effects in observational black hole astrophysics.

Rotating Charged Black Holes in Kalb-Ramond Gravity

The KR-modified black hole metric incorporates the Lorentz-violating parameter $\ell$ in the definition of $\Delta$ and $\Sigma$. At $\ell=0$, the metric reduces to Kerr-Newman. The horizon radii and the ergosphere boundaries are parametrically affected by $a$0, $a$1, and $a$2. The equations of motion for particles on the equatorial plane are derived via the Hamilton-Jacobi formalism, with these parameters directly entering the geodesics. Crucially, the radial location of energy extraction and the nature of plasma dynamics are sensitive to $a$3 through its impact on frame-dragging and the geometry within the ergosphere.

Energy Extraction in the Circular Orbit Region

Energy extraction via magnetic reconnection requires (a) accelerated plasma to escape with positive energy at infinity and (b) decelerated plasma to acquire negative energy and plunge into the horizon, i.e., Penrose-type conditions. The ZAMO frame is used to simplify the analysis, allowing for transparent computation of hydrodynamic energies per unit enthalpy.

The allowed parameter space for energy extraction is presented as a function of $a$4 and $a$5, with detailed analysis of the effects of $a$6, $a$7, $a$8 and $a$9. The numerical results demonstrate:

• Increasing $Q$0 (field orientation angle) shrinks the extraction region, while higher plasma magnetization $Q$1 expands it.
• Larger charge $Q$2 reduces the allowed region and shifts it inward.
• Most notably, increasing $Q$3 strongly restricts and shifts the extraction region; even moderate changes in $Q$4 lead to non-overlapping regions, thus amplifying the discriminative power for probing Lorentz violation.

Figure 1: Energy extraction region in the circular orbit region for varying $Q$5, $Q$6, $Q$7, and $Q$8; demonstrating the parameter space sensitivity, particularly to the Lorentz-violating parameter $Q$9.

Energy extraction power $\sigma$0 and efficiency $\sigma$1 are calculated and show similar dependencies:

• Power increases monotonically with decreasing $\sigma$2 and increasing $\sigma$3; for fixed X-point radial locations, the maximal power occurs near the photon sphere.
• $\sigma$4's effect on power is non-monotonic and depends on $\sigma$5.
• $\sigma$6 has a pronounced effect; distinct values produce disjoint power curves and efficiency profiles.

Figure 2: Energy extraction power per unit enthalpy density $\sigma$7 in the circular orbit region — manifesting peak values and shifts dependent on parameter combinations.

Figure 3: Energy extraction efficiency $\sigma$8 in the circular orbit region, exhibiting similar parameter dependence as $\sigma$9, with peak efficiencies in narrow bands near the ergosphere boundary.

Energy Extraction in the Plunging Region

When plasma migrates inward from ISCO into the plunging region, its radial velocity dominates and modifies extraction criteria. The hydrodynamic energy per unit enthalpy includes corrections for the plunging motion.

A key result is that the minimum spin required for energy extraction in the plunging region is much lower than in the circular orbit regime, and the inner spatial boundary of extraction now extends down to the event horizon rather than the photon sphere. The permitted extraction region is less sensitive to $\xi$0; only large variations in $\xi$1 yield distinct parameter spaces, meaning constraints are weaker.

Figure 4: Energy extraction region in the plunging region, with broader allowed spin intervals and weaker sensitivity to $\xi$2 compared to the circular orbit region.

Energy extraction power and efficiency in the plunging region exhibit:

• Nonzero power at the event horizon, with more complex dependence on $\xi$3 and $\xi$4.
• The effect of $\xi$5 is dampened; overlapping power curves are common unless $\xi$6 varies considerably.

Figure 5: Energy extraction power per unit enthalpy density $\xi$7 in the plunging region, with the event horizon as the inner boundary, and less pronounced parameter dependence, especially for $\xi$8.

Figure 6: Energy extraction efficiency $\xi$9 in the plunging region, mirroring power trends and showing reduced sensitivity to Lorentz-violating effects.

Implications and Theoretical Significance

The results quantitatively establish that KR-induced Lorentz violation yields observable modifications to the energetics and parameter space of black hole plasma outflows. Energy extraction from the circular orbit region is shown to be especially sensitive to $\ell$0, suggesting high-energy astrophysical jet observations, or detailed measurements of extraction efficiency and power, can serve as probes for string-inspired antisymmetric tensor fields and low-energy Lorentz violation.

For the plunging region, the broader spin interval required for extraction and weaker $\ell$1 dependence imply that observed energetic phenomena from low-spin black holes are likely associated with this regime. However, discrimination of the KR field effects is far less effective here.

The dual-region comparison underscores that magnetic reconnection not only remains a robust energy transfer mechanism in modified gravity but also offers a testbed for quantum gravity motivated field effects in strong gravity environments.

Conclusion

This paper provides a systematic, parameter-sensitive study of energy extraction via the Comisso-Asenjo mechanism in Kalb-Ramond gravity, detailing the influence of Lorentz-violating effects on extraction regions, power, and efficiency. The analysis demonstrates the circular orbit region’s potential as a precise probe for KR fields, while the plunging region, though astrophysically relevant, offers weaker constraints. These results deepen understanding of black hole energetics in string-motivated gravity extensions and motivate future observational campaigns aiming to constrain Lorentz violation and probe quantum fields in strong gravity.