Compact Stars Sourced by Dark Matter Halos and Their Frozen States

TL;DR

This work develops horizonless compact stars sourced by dark matter halos by relaxing the common $P_r=-\rho$ constraint and solving the Einstein equations for an anisotropic fluid with an Einasto density profile. It identifies two viable radial-pressure prescriptions (Case I and Case II) and demonstrates that, in certain regimes, the configurations can enter a frozen state where $g_{tt}$ becomes arbitrarily small at a finite radius, mimicking black holes without an event horizon. Axial perturbation analysis shows Case I configurations are linearly stable, while Case II can develop negative effective potentials and potential instabilities beyond specific thresholds. The results propose a robust DM-sourced mechanism for black-hole mimickers, connecting galactic DM structure to strong-gravity phenomena and observable signatures such as quasinormal modes and redshift behavior.

Abstract

Inspired by regular black holes (RBHs) sourced by dark matter halos, we generalize the anisotropic energy-momentum tensor by relaxing the $P_r = -ρ$ condition between radial pressure and density. We demonstrate that while RBHs are a unique special case, a broader class of relations yields horizonless compact stars. Under specific parameter limits, these objects approach a ``frozen state," mimicking black hole features without an event horizon. These compact star solutions could satisfy weak energy conditions and provide a robust mechanism for dark matter-sourced black hole mimickers.

Figures (7)

• Figure 1: The relationship between the minimum of $\rho +P_\perp$ and $a_0$ with the fixed parameters $\rho_0=0.5$, $n=0.5$ and $h = 0.5$.
• Figure 2: The spatial distributions of functions $-g_{tt}$, $N$, and $P_\perp$ for different values of $\rho_0$ with $a_0=0$ and $h=0.5$.
• Figure 3: Spatial distributions of the metric functions $-g_{tt}$ (dashed lines), $\sigma$ (solid lines), the radial pressure $P_r$ (dashed lines) and tangential pressure $P_\perp$ (solid lines) under varying $a_0$.
• Figure 4: The distributions of $P_\perp$ and $\sigma(r)$ under different values of $a_0$ for the frozen state at $\rho_0 = 0.6839105$, $n=0.5$, and $h=0.5$.
• Figure 5: Spatial profiles of the functions $-g_{tt}$ (dashed), $\sigma$ (solid), $P_r$ (dashed), and $P_\perp$ (solid) for two representative central densities, $\rho_0 = 0.2$ and $\rho_0 = 0.6$. The parameters are fixed as $n=1/2$, $h=1/2$, $a=2$, $m=4$, $b=1$, $k=1$, and $\gamma=6$.