Hernquist distribution of matter as a source of black-hole geometry

TL;DR

This paper investigates black-hole geometries embedded in realistic galactic dark-matter halos by enforcing a vacuum-like radial equation of state $P_r=-\rho$ on the halo fluid. Using static, spherically symmetric anisotropic-fluid spacetimes and the Misner–Sharp mass $m(r)$, the authors derive the field equations and show that $B(r)=1$ under the chosen equation of state, with $m(r)=4\pi\int_{0}^{r} x^{2}\rho(x)\,dx+ M_{0}$ and $f(r)=B(r)^2\left(1-\frac{2m(r)}{r}\right)$. They analyze several parameterizations of the Hernquist profile, finding that the resulting black-hole solutions typically retain a central singularity unless special cases (e.g., $\alpha=0,\gamma=4,k=1$ with $M_{0}=0$) are selected. Horizons and global structure depend on the halo scale $a$ and the central mass term $M_{0}$, illustrating how the choice of density profile and pressure prescription crucially shapes interior geometry. The results indicate that dark matter alone does not guarantee regular interiors and motivate further studies of observable signatures (e.g., quasinormal modes, shadows) for these embedded black holes.

Abstract

It was recently demonstrated that imposing the condition $P_{r} = -ρ$ on the radial pressure of a galactic halo can lead to regular black-hole solutions for certain density profiles, such as the Dehnen and Einasto models. In the present work, we show that some of the most commonly used halo profiles, including the Hernquist model, do not yield regular geometries under the same condition, but instead support black-hole solutions that retain a central singularity

Figures (1)

• Figure 1: Hawking temperature as a function of halo parameter $a$ for the two models: Hernquist model $\alpha=1$, $\gamma=4$, $k=1$, $M_{0}=0$ (red) and $\alpha=0$, $\gamma=4$, $k=1$, $M_{0}=0$ (blue).