Plummer Dark Matter Black Hole with Topological Defects: Shadow, Greybody Factors, Quasinormal Modes, and Thermodynamics

Abstract

We construct a static, spherically symmetric black hole (BH) solution embedded in a cored Plummer dark matter (DM) halo and a Letelier cloud of strings (CoS). Starting from the Plummer-Schwarzschild metric of Senjaya et al.~\cite{Senjaya2026}, we incorporate the string-cloud tension parameter $α$ into the lapse function, obtaining $A(r) = h_{\rm Plummer}(r) - α$. The resulting spacetime admits a single, non-degenerate event horizon (EH) for $α< 1$ and a naked singularity for $α\ge 1$. We determine the photon sphere (PS) and BH shadow radii, compute the weak deflection angle via the Gauss-Bonnet theorem (GBT), and analyze the innermost stable circular orbit (ISCO). Scalar perturbations are studied through the effective potential, greybody factor (GF) bounds obtained from the Boonserm-Visser method, the Hawking emission spectrum, and quasinormal mode (QNM) frequencies computed with the WKB approximation. The thermodynamic analysis covers the Hawking temperature, Bekenstein-Hawking entropy, heat capacity, and Gibbs free energy; the heat capacity is found to be strictly negative for all parameter values, confirming the absence of any Davies-type phase transition. A consistent hierarchy emerges across all six analyses: the CoS tension $α$ governs the leading-order modifications to every observable, while the Plummer halo density $ρ_0$ provides a subdominant, additive correction.

Figures (14)

• Figure 1: Metric function $A(r)$ for various Plummer DM and CoS parameter combinations. The black dashed horizontal line marks $A=0$. Curves that cross this line possess a single EH; those remaining entirely below it (e.g., $\alpha=1.0$ and $\alpha=1.2$) correspond to naked singularities. Parameters: $M=1$, $r_0/M=0.2$.
• Figure 2: Metric function $A(r)$ as a function of the dimensionless radial distance for various halo parameters $\{r_0,\,\rho_0\}$ and CoS tension $\alpha$. Panel (i): varying $\rho_0$ at fixed $r_0/M=0.2$ and $\alpha=0.1$. Panel (ii): varying $r_0$ at fixed $\rho_0 M^2=0.5$ and $\alpha=0.1$. Panel (iii): varying $\alpha$ at fixed $r_0/M=0.2$ and $\rho_0 M^2=0.5$. The zero crossing of each curve marks the corresponding EH radius.
• Figure 3: Null effective potential $V_{\rm eff}(r)$ as a function of the dimensionless radial coordinate for various Plummer halo parameters $\{r_0,\,\rho_0\}$ and CoS tension $\alpha$. In all panels the peak decreases and moves outward as the varied parameter grows, signaling a weakening of the photon trapping barrier. Here $\mathrm{L}/M=1$.
• Figure 4: PS radius $r_{\rm ph}/M$ (left) and shadow radius $R_{\rm sh}/M$ (right) as functions of $\{\rho_0,\,\alpha\}$ at fixed core radius $r_0/M=0.2$. Both surfaces increase monotonically with $\rho_0$ and $\alpha$, with the steeper gradient along the $\alpha$-axis reflecting the dominant role of the CoS tension.
• Figure 5: Effective radial force $\mathcal{F}$ experienced by photons as a function of the dimensionless radial coordinate for various Plummer halo parameters $\{r_0,\,\rho_0\}$ and CoS tension $\alpha$. The zero crossing of each curve marks the PS radius $r_{\rm ph}$. Here $\mathrm{L}/M=1$.