Dymnikova Black Hole Immersed in Perfect Fluid Dark Matter and a Cloud of Strings: Hawking Temperature, Dynamics and QPOs Analysis

Abstract

The Dymnikova black hole represents a regular spacetime solution interpolating between a de Sitter core and an asymptotically Schwarzschild geometry. In this work, we investigate a generalized Dymnikova black hole surrounded by perfect fluid dark matter (PFDM) and immersed in a cloud of strings (CS). We analyze how these additional matter sources modify the thermodynamic, optical, and dynamical properties of the spacetime. We derive the Hawking temperature and specific heat capacity and examine the thermal stability and phase structure of the black hole. The results reveal non-monotonic temperature behavior and parameter-dependent phase transitions. We further study photon dynamics, including the photon sphere and black hole shadow, and show that both PFDM and string cloud parameters significantly affect the shadow radius and strong-field structure. Additionally, we investigate the motion of massive test particles, circular orbits, and stability conditions. The corresponding effective potentials, specific energy, and angular momentum are analyzed. Finally, we explore quasi-periodic oscillations (QPOs) by computing the fundamental epicyclic frequencies and discuss how the model parameters encode observable astrophysical signatures.

Figures (11)

• Figure 1: The behavior of the metric function $f(r)$ as a function of dimensionless radial distance $r/M$ by varying, respectively the PFDM and CS parameters. Here $r_0/M=0.4,\,$
• Figure 2: The metric function under various conditions. Here $r_0/M=0.4$.
• Figure 3: Hawking temperature $T$ as a function of the event horizon radius $r_h$ for different values of the model parameters. The upper row corresponds to $r_0 = 0.1$, while the lower row represents $r_0 = 0.3$. In the left panels, the parameter $\alpha$ is varied with fixed $\lambda$ in the right panels, $\lambda$ is varied with fixed $\alpha$. Different colors denote different parameter values.
• Figure 4: Heat capacity $C$ as a function of the horizon radius $r_h$ for two values of $r_0$. The divergence of $C$ indicates a critical point associated with a phase transition. The parameters $\alpha$ and $\lambda$ shift the location of this critical radius and modify the thermodynamic stability region of the black hole.
• Figure 5: The behavior of the effective potential as a function of radial distance by varying $\lambda$ and $\alpha$.