Optical appearance, Hawking radiation, and Barrow thermodynamics of Letelier black hole in electromagnetic universe

TL;DR

This paper investigates a Letelier black hole embedded in an electromagnetic universe with two control parameters: the cloud of strings density $\alpha$ and the EMU strength $a$. It derives the metric structure, horizon conditions, curvature features, and embedding diagrams, and provides comprehensive predictions for shadow size, photon-ring structure, and plasma effects relevant to EHT observations. The study also analyzes Hawking radiation and greybody factors for scalars, vectors, and Dirac fields, revealing strong suppression of HR with increasing $\alpha$ and milder dependence on $a$, and it explores thermodynamics under Barrow entropy, uncovering a second-order phase transition and a Barrow-modified Joule–Thomson behavior. Collectively, the results show distinctive observational signatures of the Letelier-EMU solution and offer pathways to constrain the model with current and forthcoming high-energy and gravitational-wave data, while outlining several avenues for future extensions such as QNM computation and rotating generalizations.

Abstract

We present an investigation of a static, spherically symmetric Letelier black hole (BH) immersed in an electromagnetic universe (EMU), characterized by the cloud of strings (CoS) parameter $α$ and the EMU parameter $a$. The photon sphere and shadow radius are derived analytically, revealing how both parameters modify the apparent BH silhouette compared to the Schwarzschild case. We extend the shadow analysis to homogeneous and inhomogeneous plasma environments, demonstrating systematic reductions in the observed shadow size, and compute the weak gravitational lensing deflection angle in plasma using the Gauss-Bonnet theorem. The perturbative dynamics are investigated for scalar, electromagnetic, and Dirac fields, with quasinormal mode frequencies obtained via the sixth-order WKB approximation and greybody factors calculated using the rigorous bounds method. The resulting Hawking radiation spectra reveal distinct signatures for bosonic and fermionic emission channels. We further analyze quasi-periodic oscillations by deriving the fundamental orbital frequencies and applying both parametric resonance and relativistic precession models, obtaining constraints from observations.

Figures (15)

• Figure 1: Lapse function $f(r)$ for the Letelier BH in EMU with $M=1$. (a) Variation with CoS parameter $\alpha \in \{0.0, 0.1, 0.3, 0.5, 0.7, 0.9\}$ at fixed $a = 0.5$. (b) Variation with EMU parameter $a \in \{0.0, 0.3, 0.5, 0.7, 0.9, 1.0\}$ at fixed $\alpha = 0.1$. (c) Special limiting cases including Schwarzschild, Letelier, RN-like, and extremal configurations. The dashed gray line marks $f(r) = 0$, with intersections indicating horizon locations.
• Figure 2: 3D isometric embedding diagrams of the Letelier BH in EMU for six parameter configurations with $M = 1$. The turquoise surface represents the spatial geometry from the EH outward to $r = 15M$, the red ring marks the outer horizon $r_+$, and the black curve depicts an infalling trajectory. The funnel widens as $\alpha$ increases, reflecting the EH expansion induced by the CoS.
• Figure 3: Effective potential $V_{\text{eff}}$ for null geodesics with $L = 1$ and $M = 1$. (a) Varying $\alpha \in \{0.0, 0.1, 0.2, 0.3, 0.4\}$ at fixed $a = 0.5$. (b) Varying $a \in \{0.3, 0.5, 0.7, 0.9, 1.0\}$ at fixed $\alpha = 0.1$. The peak location corresponds to the PS radius $r_{ps}$.
• Figure 4: Shadow radius $R_{sh}/M$ as a function of the model parameters. (a) $R_{sh}$ versus CoS parameter $\alpha$ for different values of $a$. (b) $R_{sh}$ versus EMU parameter $a$ for different values of $\alpha$. The gray dashed line indicates the Schwarzschild value $R_{sh}^{\text{Sch}} = 3\sqrt{3}M$.
• Figure 5: Decomposition of the observed emission into direct, lensed, and PR contributions for varying CoS parameter $\alpha$ at fixed $a = 1$. Top row: $\alpha = 0$ (Schwarzschild limit). Middle row: $\alpha = 0.1$. Bottom row: $\alpha = 0.2$. Left column: direct emission. Middle column: lensed emission. Right column: PR. The shadow size increases with $\alpha$ in all three components, reflecting the expansion of the PS due to the CoS.