Quasinormal modes, Hawking radiation and absorption of the massless scalar field for Bardeen black hole surrounded by perfect fluid dark matter

Abstract: We study the quasinormal modes, Hawking radiation and absorption cross-section of the Bardeen black hole surrounded by perfect fluid dark matter for a massless scalar field. Our results show that the oscillation frequency of quasinormal modes is enhanced as magnetic charge $g$ or the dark matter parameter $\alpha$ increases. For damping rate of quasinormal modes, the influence of them is different. Specifically, the increase of dark matter parameter $\alpha$ makes the damping rate increasing at first and then decreasing. While the damping rate is continuously decreasing with the increase of the magnetic charge $g$. Moreover, we find that the increase of the dark matter parameter $\alpha$ enhances the power emission spectrum whereas magnetic charge $g$ suppresses it. This means that the lifespan of black holes increases for smaller value of $\alpha$ and larger value of $g$ when other parameters are fixed. Finally, the absorption cross-section of the considered black hole is calculated with the help of the partial wave approach. Our results suggest that the absorption cross-section decreases with the dark matter parameter $\alpha$ or the magnetic charge $g$ increasing.

• The paper reveals that dark matter parameter α and magnetic charge g significantly influence quasinormal modes and scalar field decay rates.
• It employs a 6th-order WKB method to compute QNMs and analyzes modifications in Hawking radiation and energy emission within a PFDM context.
• The study shows that increased spherical harmonic indices, dark matter parameters, and magnetic charge raise potential barriers, reducing scalar absorption cross-sections and affecting black hole lifespans.

Quasinormal Modes, Hawking Radiation, and Absorption of the Massless Scalar Field for Bardeen Black Holes

The paper examines the intricate dynamics of quasinormal modes (QNMs), Hawking radiation, and absorption cross-sections for massless scalar fields in the context of Bardeen black holes surrounded by perfect fluid dark matter (PFDM). This study brings to light important gravitational properties and interactions, notably influenced by the dark matter parameter $\alpha$ and the magnetic charge $g$, thereby reflecting the nuanced interplay between theoretical black hole models and their astrophysical implications.

Introduction and Background

The motivation behind this research stems from the growing observational evidence of non-singular black holes and the necessity to integrate dark matter effects into general relativity's framework. Regular black holes such as the Bardeen black hole, originally proposed to circumvent singularities, have been further explored in scenarios enveloped by PFDM, offering a richer model to test against physical phenomena like gravitational waves and the shadow images captured by the Event Horizon Telescope.

PFDM, introduced by Kiselev, presents an isotropic pressure and mass density model, pivotal in explaining anomalies in galactic rotation curves and cosmic microwave background readings. This paper extends previous work by considering Bardeen black holes merged with PFDM, establishing a mathematical and physical foundation to explore QNMs and scalar field absorption.

Mathematical Model and Methods

The analysis relies on Einstein-Maxwell equations integrated with nonlinear electrodynamics to describe the Bardeen black hole configuration in PFDM. The metric for this model is static and spherically symmetric, characterized by the function $f(r)$, incorporating contributions from both magnetic charge and dark matter parameters.

The study employs the Schrödinger-like wave equation approach to delineate the scalar field perturbations. This forms the basis for calculating QNMs using the 6th-order WKB method, a technique known for balancing computational efficiency with accuracy in perturbation analysis. The energy emission rate via Hawking radiation, similarly analyzed, adopts the WKB approach to incorporate the gray-body factors affecting the spectra received at infinity.

Analysis of Quasinormal Modes

The real and imaginary components of the quasinormal frequencies for the massless scalar field elucidate the oscillation dynamics within this framework, highlighting crucial dependencies on spherical harmonic indices $l$, dark matter parameter $\alpha$, and magnetic charge $g$. Specifically, increased $l$ and $g$ intensify the oscillation frequency and prolong damping rates, whereas variances in $\alpha$ reveal a non-linear relationship with decay rates—enhancements followed by reductions at larger values.

Hawking Radiation and Energy Emission Rates

Evaluating Hawking radiation focuses on understanding quantum thermal emissions under differing black hole parameters. The findings indicate that while both magnetic charge and spherical harmonic index suppress energy emission rates, dark matter parameters amplify these rates. This adjustment in emission characteristics correlates with modifications in lifespan predictions for such cosmic entities—increased $g$ and reduced $\alpha$ collectively extending black hole existence.

Absorption Cross-Section

The paper discusses the absorption cross-section with respect to scalar fields using the partial wave method. The cross-section decreases with higher $l$, $\alpha$, and $g$, attributable to elevated potential barriers inhibiting scalar wave transmission into black holes. The comparative analysis between total absorption cross-sections of various black hole models further underscores the influential role of PFDM and intrinsic magnetic properties.

Conclusion

The findings contribute valuable insights into our understanding of Bardeen black holes when immersed in PFDM environments. Demonstrating how dark matter parameters and magnetic charge impact the fundamental characteristics of quasinormal modes, Hawking radiation, and scalar field absorption shifts the perception of black hole dynamics from singular objects to complex, interactive systems. This work lays a theoretical foundation for future explorations into non-singular gravitational models, presenting potential pathways for integrating observed phenomena into canonical astrophysical theories.