Observational Signatures of Exact Black Hole Solutions in a Dark Matter Halo

Abstract

In this work, we derive novel exact solutions describing Schwarzschild-like black holes (BHs) embedded in a Dehnen-type dark matter (DM) halo density profile and investigate their geometric, dynamical, and observational signatures arising from such geometries. We begin by analyzing the horizon structure and spacetime curvature invariants, as well as examining the energy conditions associated with the DM halo. Subsequently, we study the influence of the DM halo on both timelike and null geodesics in the resulting geometry. Finally, we obtain observational constraints on the DM halo parameters by comparing the model predictions with weak-field data from Mercury and the S2 star orbit, as well as strong-field observations from the Event Horizon Telescope (EHT), GRAVITY, and combined (EHT+GRAVITY) datasets for M87* and Sgr A*, employing Bayesian inference and Markov Chain Monte Carlo (MCMC) methods to determine the best-fit values and corresponding upper limits of the model parameters. Our analysis provides valuable insight into probing the potential influence of DM halo environments on spacetime geometry and observable properties of astrophysical BHs, offering an alternative perspective on BH-DM interactions.

Figures (9)

• Figure 1: Left panel: The radial dependence of function $f(r)$ for various values of parameter $\gamma$ for the fixed values of the DM halo parameters $r_s=0.4$ and $\rho_s=0.3$ values. Right panel: The dependence of horizon radius on $\gamma$ for various combinations of $r_s$ and $\rho_s$.
• Figure 2: The Ricci scalar($R$) (left panel), the Ricci square ($R^2$) (middle panel), and the Kretschmann scalar (K) (right panel) as a function of r for a Schwarzschild-like BH in a DM halo for different values of $\gamma$ parameter
• Figure 3: The radial profile of the NEC, WEC, DEC and SEC for varying $\gamma$ parameter (from left to right).
• Figure 4: The effective potential $V_{\rm eff}$ for the fixed $r_s$ and $\rho_s$ (left) and $R_{\rm ISCO}$ as a function of $r_s$ for the fixed $\rho_s$ (right) for various combinations of $\gamma$.
• Figure 5: Effective potential $V_{\rm eff}(r)$ for a massive particle for various combinations of $r_s$ and $\rho_s$. Note that $(\alpha,\beta,\gamma)=(1,4,9/4)$ is considered for the density profile.