Observable signatures of black hole with Hernquist dark matter halo having a cloud of strings: geodesic, perturbations, and shadow

Abstract

We present a comprehensive theoretical investigation of a novel black hole (BH) spacetime: a Schwarzschild BH embedded in a Hernquist-type dark matter halo (HDMH) and surrounded by a cloud of strings CS-collectively termed the Schwarzschild-HDMH with CS (SHDMHCS) configuration. By analyzing the spacetime geometry, we explore how key geometrical parameters, such as, the core radius and halo density of the dark matter, along with the cloud of strings affect the geodesic motion of both massless and massive test particles. Our results show that the combined influence of HDMH and CS modifies the effective potentials for null and time-like geodesics, leading to distinct dynamical behavior compared to the standard Schwarzschild geometry. We perform a perturbative analysis for scalar (spin-0), electromagnetic (spin-1), and Dirac (spin-1/2) fields, deriving the associated effective potentials and showing how the dark matter halo and CS alter these field propagation and potential barriers. Moreover, the shadow of the selected BH is studied in detail, deriving analytical expressions for photon sphere and shadow radii, showing that CS tend to enlarge the shadow, while HDMH properties tend to shrink it. The combined effects of these parameters significantly influence the shadow's shape and size, producing potentially observable signatures. Our results establish that the SHDMHCS configuration yields distinct observational imprints detectable by present and forthcoming astrophysical instruments. This framework provides new tools for probing exotic matter distributions via gravitational wave observations, orbital dynamics, and high-resolution BH imaging, offering a pathway to distinguish such configurations from simpler BH models in realistic environments.