Thermodynamics, Weak Gravitational Lensing, and Parameter Estimation of a Schwarzschild Black Hole Immersed in Hernquist Dark Matter Halo

TL;DR

This work analyzes a Schwarzschild black hole embedded in a Hernquist dark matter halo by deriving the SBHD metric $f(r)=1-\frac{2M}{r}-\frac{4\pi \rho_s r_s^3}{r+r_s}$ and examining horizon structure, thermodynamics (including a finite evaporation remnant), weak gravitational lensing, and the black hole shadow. It demonstrates DM modifies the horizon and thermodynamic stability, and induces DM-dependent corrections to the deflection angle and shadow observables. By comparing the shadow deviation $\delta=\frac{R_s}{3\sqrt{3}M}-1$ with bounds from $M87^*$ and $Sgr A^*$ (EHT, Keck, VLTI), the authors constrain the Hernquist DM parameters $(\rho_s, r_s)$ and show a consistent parameter space where SBHD matches observations. The results illustrate how DM halos imprint observable signatures in strong-field gravity and provide a framework to bound DM near galactic centers.

Abstract

In this article, we obtain a novel black hole (BH) solution of a Schwarzschild BH immersed in a Hernquist dark matter (SBHD) halo. The thermodynamic properties of the resultant spacetime are then studied to gauge the impact of dark matter (DM) on the local and global stability of the composite system of the BH-DM halo. With the intention of finding imprints of DM, we then studied weak gravitational lensing (GL) and shadow. Both display significant dependence on the DM parameters - core radius $r_s$ and core density $ρ_s$. Finally, we constrain DM parameters by utilizing bounds on the deviation parameter $δ$ for super-massive BHs (SMBHs) $M87^*$ and $Sgr A^*$ reported by Event horizon telescope (EHT), Keck, and VLTI observatories. Our analysis finds SBHD congruent with experimental observations, thereby making it a feasible candidate for an SMBH.

Figures (11)

• Figure 1: Variation of the event horizon radius with the core density keeping $r_s=0.5M$ (left panel) and with the core radius keeping $\rho_s M^2=1.0$ (right panel).
• Figure 2: Variation of the Hawking temperature with the core density kepping $r_s=0.5M$ (left panel) and with the core radius keeping $\rho_s M^2=1.0$ (right panel).
• Figure 3: Variation of specific heat with the core density kepping $r_s=0.5M$ (left panel) and with the core radius keeping $\rho_s M^2=1.0$.
• Figure 4: Variation of free energy with the core density kepping $r_s=0.5M$ (left panel) and with the core radius keeping $\rho_s M^2=1.0$ (right panel).
• Figure 5: Schematic diagram of the quadilateral ${}_O^{\infty}\Box_{S}^{\infty}$.