Shadows of rotating non-commutative Kiselev black holes: constraints from EHT observations of M87* and Sgr A* - Fazlay Ahmed; Heena Ali; Qiang Wu; Tao Zhu; Sushant G. Ghosh (European Physical Journal C: Particles and Fields)
Abstract The Event Horizon Telescope (EHT) imaged black holes M87 $$^*$$ ∗ (angular diameter $$θ _d = 42 ± 3\,\upmu \text {as},$$ θ d = 42 ± 3 μ as , mass $$\sim 6.5 × 10^9\,M_\odot )$$ ∼ 6.5 × 10 9 M ⊙ ) and Sgr A $$^*$$ ∗ $$(θ _d = 48.7 ± 7\,\upmu \text {as},$$ ( θ d = 48.7 ± 7 μ as , shadow deviation $$δ ≈ -0.08^{+0.09}_{-0.09}$$ δ ≈ - 0 . 08 - 0.09 + 0.09 (VLTI), $$-0.04^{+0.09}_{-0.10})$$ - 0 . 04 - 0.10 + 0.09 ) (Keck). These observations enable tests of gravity in strong regimes. We propose a rotating non-commutative inspired Kiselev black hole (RNKBH), incorporating dark energy $$(ω )$$ ( ω ) and non-commutative $$(Θ )$$ ( Θ ) parameters, extending Kerr solutions. Our analysis reveals that $$ω = -2/3$$ ω = - 2 / 3 allows larger $$Θ $$ Θ but requires $$a \ge 0.16M$$ a ≥ 0.16 M to maintain horizons. Shadow calculations show significant deviations from Kerr predictions: for $$Θ = 0.001-0.005M^2,$$ Θ = 0.001 - 0.005 M 2 , shadows shrink by 8-15% and distortion increases by 20-35% for rapidly spinning $$(a > 0.5M)$$ ( a > 0.5 M ) black holes. The $$ω = -2/3$$ ω = - 2 / 3 exhibits shadow squeezing near the cosmological horizon. We compute shadow observables and compare them with EHT data. For Sgr A $$^*$$ ∗ $$(50^° $$ ( 50 ∘ inclination), the bounds are $$0.001497 \le Θ \le 0.002868\,M^2$$ 0.001497 ≤ Θ ≤ 0.002868 M 2 at $$a =0.9146$$ a = 0.9146 $$(ω = -2/3)$$ ( ω = - 2 / 3 ) . For M87 $$^*$$ ∗ $$(17^° )$$ ( 17 ∘ ) , $$0 \le Θ \le 0.004993 \,M^2$$ 0 ≤ Θ ≤ 0.004993 M 2 at $$a=0.0.6167$$ a = 0.0 . 6167 $$(ω = -2/3)$$ ( ω = - 2 / 3 ) . While EHT cannot yet distinguish RNKBH from Kerr BH, our results highlight its viability as an astrophysical candidate.