Shadow of Non-singular Rotating Magnetic Monopole in Perfect Fluid Dark matter

Abstract: Bardeen proposed a gravitationally collapsing magnetic monopole black hole solution which is free of singularity. In this article, we have studied the size and shape of the rotating Bardeen blackhole shadow in presence of perfect fluid dark matter. we have discussed how the parameters such a spin, magnetic monopole charge and influence of dark matter affects the shadow of our blackhole. The apparent shape of the blackhole was studied by using two observables, the radius Rs and the distortion parameter R_s. Further the blackhole emission rate is also studied, we found out that for rotating Bardeen in PFDM ,For a constant monopole charge, the emission rate increases with increase in dark matter parameter, the emission rate decreases with increase in magnetic charge and spin.

• The paper presents a non-singular rotating magnetic monopole model by integrating Bardeen’s approach with perfect fluid dark matter, focusing on shadow characteristics.
• It employs the Newman-Janis algorithm and Hamilton-Jacobi method to derive the metric and analyze photon orbits and effective potential stability.
• Findings indicate that increased dark matter parameter reduces shadow size while higher spin and monopole charge distort photon trajectories and lower emission rates.

Shadow of Non-singular Rotating Magnetic Monopole in Perfect Fluid Dark Matter

Introduction

The paper investigates the complex interplay between non-singular black holes, magnetic monopoles, and perfect fluid dark matter (PFDM). Specifically, it analyzes the shadow and emission characteristics of rotating Bardeen black holes under the influence of PFDM. Bardeen's model stands out for proposing a non-singular black hole solution by integrating concepts of non-linear electrodynamics with a self-gravitating magnetic monopole. The presence of dark matter, manifested as PFDM, introduces additional parameters influencing the black hole's observable characteristics such as shadow shape, size, and emission rate.

Rotating Gravitationally Collapsed Magnetic Monopole in PFDM

The paper employs the Newman-Janis algorithm to derive the metric of rotating gravitationally collapsed magnetic monopoles influenced by PFDM. This metric is pivotal for calculating photon orbit equations using the Hamilton-Jacobi variable separation method. By leveraging geodesic motion equations, it sets the framework to explore photon trajectories, crucial for understanding black hole shadows and emissions. Key equations derived include expressions for the effective potential, which dictate stability conditions of photon orbits.

Effective Potential Analysis

Effective potential plays a critical role in determining spherical orbits' stability. The paper highlights that variations in magnetic monopole charge $g$ or dark matter parameter $k$ directly affect the potential's extrema, dictating orbit stability. The notion that maximum potential energy conditions coincide with stationary orbits underpins the discussion on shadow shapes and emission rates, asserting that higher values of $g$ reduce potential differences influencing orbit stability.

Black Hole Shadows

Shadow characteristics are contingent on parameters $\alpha$ and $\beta$ derived from celestial coordinates, representing apparent dislocation of light due to gravitational lensing. The paper observes that shadow size inversely correlates with monopole charge and dark matter parameter, presenting visual evidence through graphical analysis. Shadows remain circular for non-rotating cases, with increased angular distortion noted for higher spin values, expounding on the impact of spin in conjunction with dark matter parameter variations on shadow morphology.

Energy Emission Rate

The energy emission rate is computed in terms of the limiting constant $\sigma_{lim}$, proportional to the shadow's cross-sectional area $\pi R_s^2$. Results indicate that emission rates increase with dark matter parameter $k$ and decrease with spin $a$ for constant monopole charge $g$. Conversely, for constant $k$, an increase in magnetic charge or spin reduces emission rates, establishing a critical relationship between rotating dynamics, monopole characteristics, and emission efficiency.

Conclusion

This work enhances the understanding of gravitationally collapsed, rotating magnetic monopoles within the context of PFDM. It elucidates how key parameters like monopole charge, dark matter influence, and angular momentum affect shadow dimensions and emission rates. Specifically, it finds that with constant $g$, shadow size decreases as $k$ increases, while the distortion increases with $a$. Furthermore, the emission rate anomalies underscore the profound influence of cosmic conditions on black hole radiative characteristics. This paper sets a foundation for future explorations into rotating black holes in unconventional dark matter configurations, fostering insights into astrophysical observations and theoretical models.

In summary, the study bridged astrophysical observations with theoretical models, expanding the landscape of possible non-singular black hole solutions amid dark matter effects. Future research could explore novel interactions and gauge symmetries influencing such cosmological phenomena.