Cored Navarro-Frenk-White dark matter halo: novel black hole solution, energy condition, optical properties, quasinormal modes and thermodynamics

Abstract In this work, we present an exact solution describing a static, spherically symmetric black hole immersed in a cored Navarro–Frenk–White (NFW) dark matter halo. We examine the energy conditions and find that the null, weak, strong and dominant energy conditions are all satisfied, confirming the physical plausibility of our solution. Furthermore, we examine its optical and scalar perturbation properties, highlighting their connections to the Lyapunov exponent and black hole thermodynamics. By applying the principle of least action, we derive the null geodesics to study gravitational lensing and light ring phenomena in the presence of the dark matter halo. The stability of photon orbits is analyzed using the Lyapunov exponent, which we relate to the imaginary part of the massless quasinormal modes in the eikonal limit. We also investigate the thermodynamic behavior of the black hole–dark matter system by evaluating the mass function, entropy, temperature, heat capacity, Gibbs free energy and the entropy to assess both local and global stability. Overall, our results demonstrate that the surrounding dark matter halo significantly influences the black hole’s properties, enhancing its thermodynamic stability and allowing the possibility of phase transitions.