Rotating Black Holes in Perfect Fluid Dark Matter: Horizons, Photon Orbits, and Shadows
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 kc(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 μas beam-convolved ridge diameter decreases from 42.47 to 37.88 μas 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.
Related
- Photon Motion and Shadows of Rotating Black Holes with Nonlinear Electromagnetic and Anisotropic Matter Fields
- Periodic Orbits and Their Gravitational-Wave Signatures around a Rotating Black Hole Surrounded by Perfect Fluid Dark Matter
- Photon rings and shadows of black holes with non-minimal couplings between curvature and electromagnetic field
- Shadows and Polarimetric Signatures of Rotating Simpson-Visser Black Holes with Thick Disk Illumination
- Signatures of charged rotating regular black holes: quasinormal modes, grey-body factors and shadows
BibTeX
@misc{nashed2026rotating,
title = {{Rotating Black Holes in Perfect Fluid Dark Matter: Horizons, Photon Orbits, and Shadows}},
author = {G. G. L. Nashed},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08520},
eprint = {2611.08520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08520},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rotating Black Holes in Perfect Fluid Dark Matter: Horizons, Photon Orbits, and Shadows
AU - G. G. L. Nashed
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.08520
UR - https://arxiv.org/abs/2611.08520
AB - 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(r_c)=Δ'(r_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_c/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 41^2, 81^2, and 161^2 image grids, confirms this trend: for a/M=0.9 and an inclination of 17^∘, the 20 μas beam-convolved ridge diameter decreases from 42.47 to 37.88 μas 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.
ER -