Thermal fluctuation and tidal force of scalar tensor–vector gravity charged black hole

This analysis focuses on the understanding of the thermodynamic, quantum, and dynamical properties of charged black holes (BHs) in the context of scalar–tensor–vector gravity (STVG). Considering the effect of the MOG parameter ( χ ) and the electric charge ( Q ) , we discuss how modified gravity affects the stability of BHs, the phase transitions, and the geometry of the spacetime around the BHs. Thermodynamic analysis through the heat capacity, entropy, and free energy shows the presence of multiple stability phases, where larger χ values lead to an enhancement of quantum fluctuations and a larger alteration of the equilibration, and where Q values lead to a thermodynamic stabilization. The thermodynamic analysis also shows the effect of higher-order entropy correction terms resulting important quantum effects surrounding the event horizon. The analysis of Hawking emission shows the radiation gets weaker with larger Q values and gets stronger with larger χ values. This highlights a competition between electromagnetic suppression and gravitational amplification. Also, perturbation theory analysis shows scalar and electromagnetic perturbation with χ and Q diminishing transmission probabilities by enlarging the effective potential barrier. Geodesic deviation and tidal analysis shows weaker coupling and radial symmetrical perturbation. In summary, the findings indicate that STVG demonstrates a greater range of thermodynamic behavior and more pronounced curvature effects relative to General Relativity (GR). This provides a deeper understanding of the thermodynamics of BHs, not only from STVG perspectives but also from other frameworks of modified gravity.