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Dark matter halo as a source of regular black-hole geometries

R. A. Konoplya, A. Zhidenko

TL;DR

This work develops a general framework to generate exact, curvature-regular black-hole geometries embedded in galactic dark-matter halos by enforcing the radial equation of state $P_r=-\rho$. It provides explicit regular solutions for Einasto and Dehnen-type density profiles, proves stability against axial perturbations, and analyzes observable signatures such as shadow radii and Lyapunov exponents of null geodesics. The results show that dense halo profiles yield sizable deviations from Schwarzschild in the near-horizon region, with observable implications for lensing and high-frequency gravitational spectra. The study highlights the role of halos as not only astrophysical environments but also potential sources of singularity resolution, motivating future work on polar perturbations, quasinormal modes, and lensing signatures to test these regular BHs against observations.

Abstract

We construct exact black-hole solutions free of curvature singularities, sourced by dark matter halos described by galactic density profiles. Regularity of the geometry is ensured by adopting the relation $P_{r}=-ρ$ between radial pressure and density, which is consistent with the phenomenological freedom of halo models. In particular, the sufficiently dense Einasto and Dehnen-type profiles for the dark matter halo can produce asymptotically flat solutions of singularity-free black holes embedded in the galactic environment. The resulting regular black holes surrounded by dark matter are shown to be stable under axial perturbations. We further compute the shadow radii and Lyapunov exponents associated with the photon circular orbits around these black holes.

Dark matter halo as a source of regular black-hole geometries

TL;DR

This work develops a general framework to generate exact, curvature-regular black-hole geometries embedded in galactic dark-matter halos by enforcing the radial equation of state . It provides explicit regular solutions for Einasto and Dehnen-type density profiles, proves stability against axial perturbations, and analyzes observable signatures such as shadow radii and Lyapunov exponents of null geodesics. The results show that dense halo profiles yield sizable deviations from Schwarzschild in the near-horizon region, with observable implications for lensing and high-frequency gravitational spectra. The study highlights the role of halos as not only astrophysical environments but also potential sources of singularity resolution, motivating future work on polar perturbations, quasinormal modes, and lensing signatures to test these regular BHs against observations.

Abstract

We construct exact black-hole solutions free of curvature singularities, sourced by dark matter halos described by galactic density profiles. Regularity of the geometry is ensured by adopting the relation between radial pressure and density, which is consistent with the phenomenological freedom of halo models. In particular, the sufficiently dense Einasto and Dehnen-type profiles for the dark matter halo can produce asymptotically flat solutions of singularity-free black holes embedded in the galactic environment. The resulting regular black holes surrounded by dark matter are shown to be stable under axial perturbations. We further compute the shadow radii and Lyapunov exponents associated with the photon circular orbits around these black holes.

Paper Structure

This paper contains 8 sections, 45 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Spherically symmetric dark matter distributions and generic regular black hole solutions
  3. Einasto profile
  4. Dehnen-type distributions
  5. Axial perturbations
  6. Black–hole shadow and Lyapunov exponent
  7. Discussions
  8. Conclusions

Figures (4)

  • Figure 1: Metric functions for the black hole solutions with Einasto profile $n=1/2$ (left panel) and $n=1$ (right panel): $h=0.1M$ (blue), $h=0.2M$ (green), and $h=0.3M$ (red).
  • Figure 2: Metric functions for the black hole solutions with Einasto profile for large $n$. Left panel ($n=6$): $h=10^{-8}M$ (black), $h=2\cdot10^{-8}M$ (blue), $h=3\cdot10^{-8}M$ (green), and $h=4\cdot10^{-8}M$ (red). Right panel ($n=7$): $h=2\cdot10^{-10}M$ (black), $h=4\cdot10^{-10}M$ (blue), $h=6\cdot10^{-10}M$ (green), and $h=8\cdot10^{-10}M$ (red).
  • Figure 3: Shadow radius (left panel) and Lyapunov exponents (right panel) as functions of the scale parameter $h$ in units of its maximum value $h_m$ for the black hole solutions with Einasto profile (from top to bottom): $n=1$ (cyan), $n=2$ (blue), $n=3$ (green), $n=4$ (orange), $n=5$ (red), $n=6$ (magenta).
  • Figure 4: Shadow radius (left panel) and Lyapunov exponents (right panel) as functions of the scale parameter $a$ for the black hole solutions with Dehnen-type profiles for $\alpha=0$ (from shorter to longer region of $a$): $\gamma=4$, $k=1$ (cyan), $\gamma=4$, $k=2$ (blue), $\gamma=4$, $k=3$ (green), $\gamma=5$, $k=1$ (orange), $\gamma=5$, $k=2$ (red), $\gamma=5$, $k=3$ (magenta).