Charged black hole surrounded by a galactic halo in de Sitter universe

TL;DR

This work constructs analytic Einstein-Maxwell solutions for a charged black hole embedded in a general galactic halo within a de Sitter universe. The halo is modeled as an anisotropic fluid with tangential pressure and a density that vanishes at the event and cosmological horizons, with several halo profiles (Hernquist, Burkert, NFW, Taylor-Silk, Moore) embedded via a hypergeometric term in the mass function. The authors compute the black-hole shadow and show that both the cosmological constant and halo matter modify the shadow radius in a way that depends on halo mass, scale, and concentration, providing a potential observational handle on halo properties and black hole charge. The framework generalizes previous neutral, asymptotically flat results and opens avenues for future work on stability, quasinormal modes, lensing, accretion, rotation, and more sophisticated halo models.

Abstract

Assuming a sufficiently general form for the matter distribution function of a galactic halo, we have derived solutions to the Einstein-Maxwell equations describing a charged black hole embedded in such a halo, while also allowing for a non-zero cosmological constant. These solutions generalize our earlier results for neutral black holes in asymptotically flat spacetime. As specific realizations of the general distribution, we consider the Hernquist, Navarro-Frenk-White, Burkert, Taylor-Silk, and Moore halo profiles, thereby capturing a broad range of astrophysically motivated scenarios.

Figures (4)

• Figure 1: Metric functions for the charged black hole in de Sitter universe ($Q=0.5$, $r_0=1$, $r_c=50$) with the Hernquist halo ($\alpha=1$, $\gamma=4$, $k=1$, $n=0$) for $a=5$ and $s=20$ of various masses: (from top to bottom) $M=0$ (black, Reissner-Nordström-de Sitter solution), $M=0.5$ (blue), $M=1$ (cyan), $M=1.5$ (orange), and $M=2$ (red). Shaded region corresponds to the nonzero density of the dark matter (halo).
• Figure 2: Shadow radius for the charged black hole in de Sitter universe ($Q=0.5$, $r_0=1$, $r_c=50$) with the Hernquist halo ($\alpha=1$, $\gamma=4$, $k=1$, $n=0$) for $a=5$ and $s=20$ (upper, blue) and with the Burkert halo ($\alpha=1$, $\gamma=3$, $k=2$, $n=0$) for $a=5$ and $s=30$ (lower, red). The shadow radius is measured in the units of the shadow radius for the corresponding Reissner-Nordström-de Sitter black hole ($R_0\approx2.8445$). Solid lines correspond to the analytic approximations $R_s=R_0(1+A_0M/a)$, where $A_0=1.5$ for the Hernquist halo and $A_0\approx0.78$ for the Burkert halo.
• Figure 3: Shadow radius for the uncharged black hole in de Sitter universe ($Q=0$, $r_c=100r_0$) with the Hernquist model of the halo ($s=20r_0$). From top to bottom: $a=5r_0$, $a=6r_0$, $a=7r_0$, $a=8r_0$, $a=9r_0$, and $a=10r_0$. The shadow radius is measured in the units of the shadow of the Schwarzschild black hole of the same size.
• Figure 4: Shadow radius for the uncharged black hole in de Sitter universe ($Q=0$, $r_c=100r_0$) with various models of halo of the same size, $s=4a=20r_0$. From top to bottom: • the Hernquist model with $\alpha=1$, $\gamma=4$, $k=1$, $n=0$ (magenta); • the Taylor-Silk model with $\alpha=3/2$, $\gamma=3$, $k=3/2$, $n=0$ (red); • the Moore model with $\alpha=7/5$, $\gamma=14/5$, $k=7/5$, $n=0$ (orange); • the Burkert model with $\alpha=1$, $\gamma=3$, $k=2$, $n=0$ (green); • the Navarro-Frenk-White model with $\alpha=1$, $\gamma=3$, $k=1$, $n=0$ (blue). The shadow radius is measured in the units of the shadow of the Schwarzschild black hole of the same size.