Rotating Regular Black Hole Solution (1404.6443v1)

Abstract: Based on the Newman-Janis algorithm the Ayon-Beato-Garcia spacetime metric of the regular spherically symmetric, static and charged black hole has been converted into rotational form. It is shown that the derived solution for rotating regular black hole is regular and the critical value of the electric charge $Q$ for which two horizons merge into one sufficiently decreases in the presence of nonvanishing angular momentum $a$ of the black hole.

• The paper presents a derivation of a rotating regular black hole solution using the Newman-Janis algorithm, effectively eliminating singularities.
• It demonstrates that increased angular momentum lowers the critical threshold charge for merging horizons, altering the lapse function and metric components.
• The study also examines weak energy condition violations and ergosphere modifications, contributing to our understanding of black hole thermodynamics and stability.

Rotating Regular Black Hole Solution

The paper "Rotating Regular Black Hole Solution" addresses a significant topic within the domain of general relativity and black hole physics. Focusing on regular black holes, which are singularity-free solutions of Einstein's equations coupled with nonlinear electrodynamics, this work extends a solution previously presented by Ayón-Beato and García into the field of rotating black holes. The authors employ the Newman-Janis algorithm to derive a rotating version of these regular black holes from their static counterparts, a methodology that has proven effective for generating rotating solutions like the Kerr solution from the Schwarzschild metric.

Methodology

The paper methodically applies the Newman-Janis algorithm to convert the Ayón-Beato-García spherically symmetric, static black hole metric into a rotational form. This approach involves transforming coordinates into advanced Eddington-Finkelstein coordinates, formulating null tetrads, implementing complex coordinate transformations, and reverting to the Boyer-Lindquist coordinates with subsequent adjustments to ensure reality conditions. This technique allows the derivation of a rotational metric while maintaining its regularity across the spacetime, eliminating singularities that traditionally arise in classical solutions.

Results

One of the noteworthy outcomes is the determination of the critical value of the electric charge $Q$, which affects the horizon structure of the rotating regular black hole. With increases in the angular momentum $a$, the threshold charge for which two horizons merge diminishes, implying that rotational dynamics significantly alter the horizon's attributes. The paper provides an exhaustive analysis of the behavior of the lapse function $\tilde{f}(r)$ as well as $g_{rr}$ and $g_{tt}$ components, elucidating how these change with respect to the radial coordinate, rotation parameter, and electric charge.

Additionally, the work investigates the weak energy condition in the context of these rotating black holes, noting regions near the origin where violations occur. The influence of rotation on the ergosphere size and shape is also scrutinized, with findings indicating expansion proportional to charge increases.

Implications

By extending the regular black hole solutions into rotating scenarios, the authors open new avenues for studying causal structures and particle motion in such systems. This can potentially enhance our understanding of black hole thermodynamics, radiation processes near horizons, and gravitational wave emissions. The demonstrated linkage between vacuum solutions and non-vacuum dynamics may inspire further theoretical exploration into energy conditions and stability analyses within modified gravitational theories.

Future Work

Potential investigations could involve comparing the derived rotating solutions to Kerr naked singularities to explore physical phenomena unique to regular spacetimes, including gravitational lensing effects and accretion disk properties. Moreover, refining computational frameworks to simulate astrophysical processes around such regular rotating black holes could yield insights relevant to observational astronomy, particularly with the advent of advanced telescopic and detection technologies.

Conclusion

The authors successfully employ the Newman-Janis algorithm to derive a rotating black hole model from a regular solution, addressing singularity issues inherent to conventional solutions. This work contributes to the broader understanding of black hole physics by demonstrating a viable path toward regularization, evidencing the profound influence of angular dynamics on charge-dependent horizon properties. Such research plays a critical role in the pursuit of a coherent theoretical model of gravitational interactions in environments characterized by extreme conditions.