Black holes immersed in modified Chaplygin-like dark fluid and cloud of strings: shadows, quasinomal modes and greybody factors

TL;DR

The paper develops a unified framework to study black holes embedded in a composite environment of a modified Chaplygin-like dark fluid and a cloud of strings, focusing on three observables: shadows, quasinormal modes, and greybody factors. The authors introduce the MCDF-CoS metric with f(r)=1 - 2M/r - a + G(r), analyze critical photon orbits and optical appearances under spherical accretion, and compute QNMs with higher-order WKB and Pöschl-Teller methods, validating the eikonal photon-sphere correspondence. They systematically map how the CoS parameter a and MCDF parameters A and B alter shadow radii, QNM frequencies and damping, and GBF spectra, showing that a dominates across observables while A and B induce nuanced, regime-dependent effects tied to near-horizon and cosmological scales. The results establish a coherent wave-geometry relationship and offer concrete predictions for constraining exotic environments around black holes via shadow imaging, gravitational-wave ringdown, and Hawking-radiation-like scattering, with implications for future extensions to rotating spacetimes and additional perturbations.

Abstract

We present a unified investigation of black hole shadows, quasinormal modes (QNMs), and greybody factors (GBFs) for a static, spherically symmetric black hole within a composite environment of a modified Chaplygin-like dark fluid (MCDF) and a cloud of strings (CoS). We examine the structure of critical photon orbits and the corresponding optical appearance under spherical accretion. Using the Wentzel-Kramers-Brillouin (WKB) approximation, we compute the quasinormal frequencies and greybody spectra, and explore their correspondence with the black hole shadows in the eikonal limit. A systematic parameter study demonstrates that the CoS intensity has the primary influence on the shadows, QNMs and GBFs, while the MCDF parameters introduce more complex but characterizable modifications to each. Our results demonstrate that these environmental components imprint distinct yet interrelated signatures on key observables, offering specific predictions for probing exotic black hole environments.

Figures (8)

• Figure 1: The lapse function $f(r)$ for diverse parameter configurations. The first panel displays an MCDF-CoS reference case with $a=0.2$, $A=1$, $B=10^{-5}$, $\beta=0.8$, $Q=0.5$, alongside specific limits: MCDF ($a=0$), GCDF ($a=0$, $A=0$, $\beta\neq1$), CDF ($a=0$, $A=0$, $\beta=1$), and Schwarzschild-de Sitter ($a=0$, $Q=0$). Subsequent panels vary individual parameters while maintaining others at reference values.
• Figure 2: Profiles of the specific intensity $I_{\rm{obs}}(b)$ (left panels) and corresponding images (right panels) for static spherical accretion, viewed face-on by an observer near the pseudo-cosmological horizon.
• Figure 3: Profiles of the specific intensity $I_{\rm{obs}}(b)$ (left panels) and corresponding images (right panels) for infalling spherical accretion, viewed face-on by an observer near the pseudo-cosmological horizon.
• Figure 4: Effective potentials (left) and corresponding fundamental ($n=0$, $l=1$) QNM frequencies (right) for the reference models. Model parameters are detailed in Table \ref{['tab:referencemodes']}.
• Figure 5: Evolution of the fundamental ($n=0$, $l=1$) QNMs under parameter variation. From left to right: modifications to the effective potential $V(r)$; the resulting frequency shifts presented on a fixed scale; and the same data on optimized scales to resolve detailed behaviors. The black dot in each panel indicates the reference MCDF-CoS configuration ($a=0.2$, $A=1$, $B=10^{-5}$, $\beta=0.8$, $Q=0.5$).