Perturbations and Greybody Factors of AdS Black Holes with a Cloud of Strings Surrounded by Quintessence-like Field in NLED Scenario

TL;DR

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Abstract

The discovery of gravitational waves and advances in black hole imaging have opened new opportunities to probe exotic physics in strong-field regimes. Building upon a recent black hole solution in Einstein gravity coupled with nonlinear electrodynamics and exotic matter sources-specifically a cloud of strings and a quintessence field--we study the perturbative dynamics, thermodynamic behavior, and quantum transmission characteristics in anti-de Sitter spacetime. The black hole, defined by its mass, nonlinear magnetic charge, string cloud, and quintessence parameters, exhibits modified spacetime geometry, horizon structure, Hawking temperature, and effective potentials governing field propagation. We derive Schrödinger-like equations for massless scalar, electromagnetic, and fermionic perturbations, exploring how these sources jointly shape the potential barriers. The Hawking temperature shows strong dependence on the horizon radius and nonlinear charge, differing markedly from asymptotically flat cases due to the cosmological constant. Greybody factors, describing Hawking radiation transmission probabilities, are computed for all field spins via turning point analysis. A notable result arises in the fermionic sector: positive and negative helicity modes attain maximal transmission at distinct quintessence normalization values, revealing helicity-dependent coupling absent in bosonic channels. This asymmetry suggests a potential observational signature of spin-exotic matter interactions, offering new insights into detecting quintessence through black hole radiation spectra. Our results extend previous perturbative analyses by incorporating nonlinear electrodynamics, cosmic strings, and quintessence effects--linking quantum radiation studies to gravitational wave astronomy and early-universe cosmology.

Figures (20)

• Figure 1: Metric function $f(r)$ as a function of radial coordinate $r$ for various BH configurations characterized by different CS parameter $\alpha$ and NLED charge parameter $k$ values. Parameters: $M = 1$, $w = -2/3$, $\Lambda = -0.001$, $\mathrm{N} = 0.01$. The zeros of $f(r)$ correspond to horizon locations listed in Table \ref{['tab:horizons_M_alpha_k']}. Configurations with $k = 0$ exhibit single horizons (extremal), while $k > 0$ produces two distinct horizons (inner Cauchy and outer event horizons). Increasing $\alpha$ shifts the metric function downward, reflecting weakened effective gravity due to the CS. All curves asymptotically approach $-\infty$ as $r \to \infty$ due to the negative cosmological constant characteristic of AdS spacetime. The legend indicates the specific $(\alpha, k)$ values for each curve.
• Figure 2: Density plot of Hawking temperature $T_H$ as a function of event horizon radius $r_h$ and NLED charge parameter $k$ for the AdS-NLED-CS-QF BH. Parameters: $M = 1$, $\alpha = 0.2$, $w = -2/3$, $\Lambda = -0.001$, $\mathrm{N} = 0.01$. The color bar indicates temperature values (in units where $G = c = \hbar = k_B = 1$), with blue representing lower temperatures and red representing higher temperatures. The plot demonstrates that Hawking temperature increases with both horizon radius and NLED charge parameter, reflecting the interplay between AdS geometry, NLED, CS, and QF contributions to the surface gravity.
• Figure 3: Behavior of the scalar perturbative potential $\mathcal{V}_\text{scalar}$ for $\ell=0$-state by varying values of $\alpha, w$ and $k$. Here $M=1,\,\Lambda=-0.001,\,\mathrm{N}=0.01$. Panel (i) shows the effect of varying CS parameter $\alpha$ while keeping $Q=1$ and $w=-2/3$ fixed. Panel (ii) demonstrates the influence of quintessence parameter $w$ with fixed $\alpha=0.1$ and $k=0.5$. Panel (iii) illustrates the impact of NLED charge parameter $k$ with $\alpha=0.1$ and $w=-2/3$.
• Figure 4: Behavior of the scalar perturbative potential $\mathcal{V}_\text{scalar}$ for $\ell=1$-state by varying values of $\alpha, w$ and $k$. The dipole mode exhibits a pronounced centrifugal barrier compared to the monopole case in Fig. \ref{['fig:1']}, with potential peaks occurring at larger radii and achieving higher maximum values.
• Figure 5: Behavior of the scalar perturbative potential $\mathcal{V}_\text{scalar}$ for $\ell=2$-state by varying values of $\alpha, w$ and $k$.