Rotating black holes in perfect fluid dark matter: Horizons, photon orbits, and shadows

Document Type

Article

Publication Date

2-2027

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 c( a ), obtained from the degenerate-horizon conditions Δ(rc)=Δ′(rc)=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, kc/M≃2.8828(1−a/M)1.5377 is only an empirical fit over 0.90 ≤ a / M ≤ 0.999, 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 412, 812, and 1612 image grids, confirms this trend: for a/M=0.9 and an inclination of 17∘, the 20 μ as beam-convolved ridge diameter decreases from 42.47 to 37.88 μ 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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