Black hole surrounded by perfect fluid dark matter in STV gravity: particle dynamics, thermodynamics, gravitational weak lensing and EHT tests

In this work, we explore the physical and observational properties of a static, spherically symmetric black hole solution in scalar–tensor–vector gravity (STVG), also known as modified gravity (MOG), in the presence of perfect fluid dark matter (PFDM). We analyze the motion of magnetized and neutral particles, focusing on the effective potential, innermost stable circular orbits (ISCO), and energy extraction efficiency via the Novikov–Thorne accretion model. Our results show that the MOG parameter \(\alpha \) and the PFDM parameter \(\lambda \) significantly influence the particle dynamics, stability conditions, and the efficiency of energy extraction. We also investigate thermodynamic quantities such as Hawking temperature, entropy, heat capacity, and Gibbs free energy, and find that PFDM and MOG parameters critically affect the black hole’s thermal stability and phase transitions. Additionally, we study gravitational lensing in uniform and non-uniform plasma environments and compute light deflection angles modified by both MOG and PFDM effects. Finally, we analyze the shadow cast by the black hole and compare it with Event Horizon Telescope (EHT) observations of M87* and Sgr A*, providing constraints on the MOG and PFDM parameters. Our results suggest that while general relativity remains a good approximation, small deviations due to modified gravity and surrounding dark matter effects cannot be ruled out.