Quantum improved wormholes in the Dekel-Zhao dark matter halo

TL;DR

The paper investigates traversable wormholes sourced by a Dekel–Zhao dark matter halo within Asymptotically Safe Gravity (ASG). It implements the infrared running of the Newton constant with $k(r)=ξ/r$, giving $G(r)=G_0 r^2/(r^2+ξ^2)$, and inserts this into the Einstein equations with the DZ density as the source. It finds that flare-out and asymptotic flatness hold only in restricted parameter domains, with radial null energy condition violation at the throat and tangential NEC satisfaction, while ASG corrections concentrate curvature near the throat and are mirrored in embedding diagrams; a quantum force term $\mathcal{F}_Q=-G'(r)P_r$ contributes to equilibrium via a modified TOV equation. Phenomenologically, the shadow radius $R_{sh}$ increases roughly linearly with $ξ$, and values around $ξ/M\in[0.8,0.9]$ can reproduce the EHT bounds for Sgr A*, indicating a potential observable imprint of IR quantum gravity in strong-field astrophysical settings.

Abstract

This work presents and investigates novel traversable wormhole solutions within the framework of Asymptotically Safe Gravity (ASG), sourced by a dark matter halo modeled by the Dekel--Zhao density profile. The scale-dependent gravitational coupling $G(k)$, derived from the ASG renormalization group flow in the infrared regime, is incorporated directly into the field equations, providing a consistent description of quantum gravitational corrections even at astrophysical scales. The combined effects of the running coupling (parameterized by $ξ$) and the dark matter characteristics determine the geometric structure and physical viability of the wormhole. The solutions satisfy the flare-out and asymptotic flatness conditions within restricted parameter domains, exhibiting enhanced curvature near the throat due to ASG corrections. Null Energy Conditions are necessarily violated at the throat, and stability analysis based on the adiabatic sound speed as well as the modified Tolman--Oppenheimer--Volkoff equation reveal that quantum effects from ASG counteract the destabilizing influence of dark matter. Phenomenologically, the wormhole shadow radius increases nearly linearly with $ξ$, lying within the Event Horizon Telescope bounds for Sgr~A$^*$ when $ξ/M \simeq 0.8--0.9$, thus suggesting that ASG-corrected wormholes may represent observable signatures of quantum gravity in the strong-field regime.

Figures (13)

• Figure 1: The Dekel-Zhao's dark matter density profile, $\rho$, for different keys parameters as a function of $r$, with: (a) $\rho_0 = 0.01$ and $r_c =3.0$. (b) $\rho_0 = 0.01$ and $a =1.0$. (c) $a = 1.0$ and $r_c =3$. The $b = 1$ and $\gamma = 3$ are fixed.
• Figure 2: The flare-out, $[S(r)-S'(r)r]/S^2$, and asymptotic conditions with variations of $\rho_0$ and $r_c$, for $a=1.0$, $\xi = 0.1$ and $r_0 = 1.0$ fixed. (a)-(b) $\rho_0=0.01,\,0.012,\,0.015, \,0.02$ ($r_c=3.0$) and (c)-(d)$r_c=1.1,\,2.0,\,3.0,\,5.0$ ($\rho_0=0.01$) .
• Figure 3: The flare-out, $[S(r)-S'(r)r]/S^2$, and asymptotic conditions with variations of $a$ and $\xi$, for $\rho_0=0.01$, $r_c = 3$ and $r_0 = 1.0$ fixed. (a)-(b) $a=0.0,\,0.5, \,1.5, \,2.0$ ($\xi=0.1$) and (c)-(d) $\xi=0.1,\,0.5,\,0.9,\,1.5$ ($a=1.0$) .
• Figure 4: Ricci's scalar as a function of the radial coordinate, produced for Dekel-Zhao's dark matter density profile: (a) $\xi = 0, 0.5, 0.8, 1.0$($a=1.0, r_c= 2.2, \rho_0 = 0.01)$. (b) $\rho_0 = 0.008, 0.01, 0.013, 0.015$ ($a = 1.0, r_c = 2.2, \xi = 0.5$). (c) $a = 0.8, 1.0, 1.3, 1.5$ ($\rho_0 = 0.01, r_c = 2.2, \xi = 0.5$). (d) $r_c = 2.0, 2.2, 2.4, 2.6$ ($a=1.0, \rho_0 = 0.01, \xi = 0.5$). In all panels $r_0 = 1.0$.
• Figure 5: Embedding diagrams of a wormhole produced for Dekel-Zhao's dark matter density profile. (a) $a=0.0,\,1.0,\,1.5$ ($\xi=0.1,\ \rho_0=0.01,\ r_c=3.0$). (b) $\xi=0.1,\,0.5,\,0.9$ ($a=1.0,\ \rho_0=0.01,\ r_c=3.0$). (c) $\rho_0=0.01,\,0.012,\,0.015$ ($a=1.0,\ \xi=0.1,\ r_c=3.0$). (d) $r_c=1.1,\,2.0,\,3.0$ ($a=1.0,\ \xi=0.1,\ \rho_0=0.01$). (e) The 3D embedding for $a=1.0,\ \xi=0.1,\ \rho_0=0.01,\ r_c=1.1$. In all panels $r_0=1.0$.