Rotating Black Holes in Perfect Fluid Dark Matter: Horizons, Photon Orbits, and Shadows

G. G. L. Nashed

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arXiv · 2611.08520

Rotating Black Holes in Perfect Fluid Dark Matter: Horizons, Photon Orbits, and Shadows

G. G. L. Nashed

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Abstract

We investigate rotating black holes surrounded by perfect-fluid dark matter (PFDM), described by the parameter $k$, and determine the Kerr-connected region of the $(a/M,k/M)$ parameter space that contains an event horizon. The critical value $k_{\mathrm c}(a)$, obtained from the degenerate-horizon conditions $Δ(r_{\mathrm c})=Δ'(r_{\mathrm c})=0$, defines the boundary between black-hole and horizonless configurations. We derive an exact parametric form of this extremal boundary and show that its near-Kerr behavior includes a logarithmic correction; therefore, $k_{\mathrm c}/M\simeq2.8828(1-a/M)^{1.5377}$ is only an empirical fit over $0.90\leq a/M\leq0.999$, not an asymptotic scaling law. For horizon-bearing solutions, we calculate unstable spherical photon orbits and the shadow's mean radius, area, and distortion, finding that increasing $k/M$ shifts the photon region inward and reduces the shadow size. Backward ray tracing through a phenomenological optically thin disk, tested on independent $41^2$, $81^2$, and $161^2$ image grids, confirms this trend: for $a/M=0.9$ and an inclination of $17^\circ$, the $20~μ\mathrm{as}$ beam-convolved ridge diameter decreases from $42.47$ to $37.88~μ\mathrm{as}$ as $k/M$ increases from 0 to $0.08$, with the two finest grids agreeing to within $0.5\%$. Thus, PFDM produces a consistent contraction from the horizon and photon region to the geometric shadow and image ridge, although these illustrative images do not provide an Event Horizon Telescope constraint because they lack a self-consistent emission model and interferometric likelihood analysis.

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BibTeX RIS

G. G. L. Nashed. 2026-10-29. Rotating Black Holes in Perfect Fluid Dark Matter: Horizons, Photon Orbits, and Shadows. https://arxiv.org/abs/2611.08520

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