Impact of dark matter halo on black hole: Thermodynamical properties and photons motion

Abstract

This paper investigates the thermodynamic properties of a Schwarzschild black hole (BH) surrounded by a dark matter (DM) halo, modeled using a Dehnen-type density profile. Specifically, we analyze the influence of the halo's core density ${\rho }_s$ and scale radius $r_s$ on key thermodynamic quantities, including the black hole's mass, temperature, heat capacity, entropy, and Gibbs free energy. Our results show that the presence of dark matter introduces notable modifications to the black hole's thermodynamics while preserving the fundamental entropy-area relation. Additionally, we examine the effects of the DM halo on the radius of circular photon orbits, the black hole's shadow radius, and the energy emission rate.