Black Hole in Cored Plummer Dark Matter Environment: Novel Solution, Light Ring, Shadow, Lensing, Lyapunov Exponent, Eikonal Quasinormal Modes and Thermodynamics-Phase Transition

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.