Spinning black holes in astrophysical environments

Abstract

We present stationary and axially-symmetric black hole solutions to the Einstein field equations sourced by an anisotropic fluid, describing rotating black holes embedded in astrophysical environments. We compute their physical properties, including quantities associated with the circular geodesics of massless and massive particles, analyze their shadows and image features, and energy conditions. Overall, we find that deviations from the Kerr metric grow with spin.

Figures (4)

• Figure 1: Profiles for the eigenvalues of the stress-energy tensor, $\varepsilon$, $p_1$ and $p_2$, for a solution with $J/M_{\rm BH}^2 \approx 0.805$, $M_{\rm halo} \approx 10 M_{\rm BH}$, and $a_0 \approx 100 M_{\rm BH}$, at the equatorial plane, $\theta=\pi/2$.
• Figure 2: Critical curves (dashed lines), and $n=1$ lensing bands (colored regions) for a Kerr BH (gray) and for galactic BHs with $M_{\rm halo} \approx 10M_{\rm BH}$, for compactnessess $M_{\rm halo}/a_0 \approx 10^{-1}$ (red) and $M_{\rm halo}/a_0 \approx 10^{-2}$ (blue). The spin of the BHs is $J/M_{\rm BH}^2 \approx 0.44$. The darker colored regions correspond to the intersection between the different lensing bands.
• Figure 3: Convergence tests for a solution with $J/M_{\rm BH}^2 \approx 0.635$, $M_{\rm halo}\approx 10M_{\rm BH}$, and $a_0 \approx 100 M_{\rm BH}$. The resolution in the angular coordinate is fixed as $N_\theta=4$.
• Figure 4: $b'(x)$ as a function of $x=1-2r_H/r$, for $M_{\rm halo} = 10r_H$, and two distinct values of $a_0$. We observe steep gradients when $a_0$ is large. For comparison, in the vacuum GR case, $b(x)=(3-x)/2$, such that $b'(x)=-1/2$.