Black Hole Solutions with Dark Matter Halos in the Four-Dimensional Einstein-Gauss-Bonnet Gravity

Black holes (BHs) convey information about different matter-energy distributions in their immediate environment, as they bear the imprints of the intrinsic spacetime geometry and exotic surrounding matter. In this regard, exact spherically symmetric regular black hole (BH) solutions supported by two phenomenological distributions of dark matter galactic halos in Eintein-Gauss-Bonnet gravity are explored. Analytical solutions for the metric and the corresponding thermodynamic properties, including heat capacity ($C_{+}$), Gibbs' free energy ($F_{+}$), and Hawking temperature ($T_{+}$) associated with the BH's horizon radius and quasinormal modes (QNMs) are found. The specific heat is investigated, and it is discovered that a Hawking-Page phase transition with divergent $C_{+}$ occurred at a critical radius, $r_{+}^c$. Consequently, the authors have regular BHs with Cauchy and event horizons, and evaporation results in thermodynamically stable double-horizon BH remnants with zero temperatures. The QNMs of the scalar field perturbations on the regular background of the BHs are then discussed comprehensively.