A new exact static and spherically symmetric black hole solution embedded in a cored Plummer dark matter halo is constructed. The impact of the cored Plummer dark matter halo on photon dynamics and its stablity, black hole shadow, eikonal limit quasinormal modes and black hole thermodynamics-phase transition are investigated. Light rings, gravitational lensing and shadow formation are studied based on the null geodesics which is derived via the principle of least action. The stability of circular photon orbits is characterized by the Lyapunov exponent, which is shown to control the imaginary part of massless quasinormal mode frequencies. The thermodynamic properties of the black hole-dark matter system are examined through the mass function, the analog black hole’s enthalpy, entropy, temperature, heat capacity and Gibbs free energy, from which the black hole phase transition is investigated. We analytically and graphically show how the cored Plummer dark matter halo modifies the black hole’s optical and thermodynamic behavior, enhancing null geodesic and thermodynamic stability also allowing phase transitions absent in pure Schwarzschild solution.

We investigate the interplay between the weak gravity conjecture (WGC) and weak cosmic censorship conjecture (WCCC) for Reissner-Nordström anti-de Sitter (RN-AdS) black holes surrounded by perfect fluid dark matter (PFDM) within restricted phase space thermodynamics (RPST) and conformal field theory (CFT) thermodynamics frameworks. The WGC ensures that gravity must be the weakest force in any consistent quantum gravity theory, while the WCCC asserts that singularities from gravitational collapse must be hidden behind event horizons. We derive complete thermodynamic descriptions including mass, temperature, entropy, and free energy in both formalisms, accounting for PFDM parameterized by γ . Our analysis reveals characteristic swallowtail patterns in free energy curves, indicating van der Waals-like first-order phase transitions under specific parameter conditions. We demonstrate that the PFDM parameter γ and AdS radius ℓ play crucial roles in satisfying both conjectures. Significantly, we find that the compatibility range for WGC in CFT thermodynamics ( 3 ℓ < γ < 10 ℓ ) is substantially wider than in RPST ( 2 / 3 ℓ < γ < 5 ℓ ). This result suggests that the holographic dictionary acts as a natural filter for Swampland constraints, rendering the boundary CFT description more fundamental for consistency checks than the bulk thermodynamic variables. At critical points of black hole parameters, we verify simultaneous satisfaction of WGC and WCCC, demonstrating robustness within the critical framework. Our results provide compelling evidence that the holographic boundary description naturally encodes quantum gravity consistency conditions more efficiently than bulk thermodynamic formalisms, with perfect fluid dark matter serving as a crucial mediator enabling the reconciliation of these fundamental principles.

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