Eur. Phys. J. C (2025) 85: 795
https://doi.org/10.1140/epjc/s10052-025-14510-5

Regular Article - Theoretical Physics

Shadows of rotating non-commutative Kiselev black holes: constraints from EHT observations of M87* and Sgr A*

¹ Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, 310023, Hangzhou, China
² Centre for Theoretical Physics, Jamia Millia Islamia, 110025, New Delhi, India
³ United Center for Gravitational Wave Physics (UCGWP), Zhejiang University of Technology, 310032, Hangzhou, China
⁴ Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics, and Computer Science, University of KwaZulu-Natal, Private Bag 54001, 4000, Durban, South Africa

^a wuq@zjut.edu.cn

Received: 6 May 2025
Accepted: 6 July 2025
Published online: 23 July 2025

Abstract

The Event Horizon Telescope (EHT) imaged black holes M87$_{}^{\ast }$ (angular diameter ${\theta }_d=42\pm 3\mathrm{\mu }\text{as},$ mass $\sim 6.5\times {10}^9{M}_{\odot })$ and Sgr A$_{}^{\ast }$$({\theta }_d=48.7\pm 7\mathrm{\mu }\text{as},$ shadow deviation $\delta \approx -0.{08}_{-0.09}^{+0.09}$ (VLTI), $-0.{04}_{-0.10}^{+0.09})$ (Keck). These observations enable tests of gravity in strong regimes. We propose a rotating non-commutative inspired Kiselev black hole (RNKBH), incorporating dark energy $(\omega )$ and non-commutative $(\mathrm{\Theta })$ parameters, extending Kerr solutions. Our analysis reveals that $\omega =-2/3$ allows larger $\mathrm{\Theta }$ but requires $a\ge 0.16M$ to maintain horizons. Shadow calculations show significant deviations from Kerr predictions: for $\mathrm{\Theta }=0.001-0.005M^2,$ shadows shrink by 8-15% and distortion increases by 20-35% for rapidly spinning $(a>0.5M)$ black holes. The $\omega =-2/3$ exhibits shadow squeezing near the cosmological horizon. We compute shadow observables and compare them with EHT data. For Sgr A$_{}^{\ast }$$({50}^{\circ }$ inclination), the bounds are $0.001497\le \mathrm{\Theta }\le 0.002868M^2$ at $a=0.9146$$(\omega =-2/3)$. For M87$_{}^{\ast }$$({17}^{\circ })$, $0\le \mathrm{\Theta }\le 0.004993M^2$ at $a=0.0.6167$$(\omega =-2/3)$. While EHT cannot yet distinguish RNKBH from Kerr BH, our results highlight its viability as an astrophysical candidate.