Black hole in the Dekel-Zhao dark matter profile

Abstract

Motivated by the work of Cardoso et al. [Phys. Rev. D 105 (2022) 6, L061501, https://doi.org/10.1103/PhysRevD.105.L061501] on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for $r\ll r_{\mathrm{c}}$ (\textcolor{black}{$r_{\mathrm{c}}$ is a characteristic radius}), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for $r\gg r_{\mathrm{c}}$, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. \textcolor{black}{The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ($M_{\mathrm{BH}}$), while higher central densities (${\rho }_{\mathrm{ch}}$) result in smaller shadows, reflecting the environmental impact of dense dark matter halos.} Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ($r_{\mathrm{c}}$). Smaller $r_{\mathrm{c}}$ values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

8 pages, 4 figures

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