Quasinormal modes and shadow of Schwarzschild black holes embedded in a Dehnen type dark matter halo exhibiting string cloud

TL;DR

This study analyzes how a Dehnen-type dark matter halo and string cloud influence the quasinormal modes and shadow of Schwarzschild black holes, providing insights into their observational signatures and parameter constraints.

Contribution

It introduces a detailed analysis of black hole perturbations and shadow characteristics within a dark matter halo with a string cloud, using the WKB method and observational data.

Findings

Dark matter and string cloud increase photon sphere and shadow radius.

Quasinormal modes are affected by core density and string parameters.

Observational data constrains black hole parameters.

Abstract

In this paper, we consider a static spherically symmetric black hole (BH) embedded in a Dehnen-(1,4,0) type dark matter (DM) halo in the presence of a cloud string. We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes (QNMs) and shadow cast. To do this, we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins: massless scalar field, electromagnetic field, and gravitational field. Then, using the 6th order WKB approximation, we examine quasinormal modes of the BH disturbed by the three fields and derive quasinormal frequencies. The changes of QNM versus the core density parameter and the cloud string parameter for three disturbances are explored. We also investigate how the core density and the cloud string parameters affect the photon sphere and shadow radius. Interestingly, the study shows that the influence of Dehnen type DM and cloud string increases both photon spheres and shadow radius. Finally, we employ observational data from Sgr $A{^\star}$ and $M87{^\star}$ to set limitations on the BH parameters.