Astrophysical Constraints on Charged Black Holes in Scalar--Tensor--Vector Gravity

TL;DR

This work probes charged black holes in Scalar-Tensor-Vector Gravity (STVG/MOG), focusing on how the STVG coupling $\alpha$ and electromagnetic charge $Q$ shape horizon structure, light propagation, lensing in vacuum and plasma, quantum-corrected thermodynamics, strong lensing, shadows, energy emission, and accretion-disk radiative properties. Employing a topological Hawking-temperature derivation, Gauss-Bonnet lensing, quantum-corrected entropy, Bozza strong-lensing formalism, and relativistic thin-disk models, the authors show that $\alpha$ universally enhances gravitational effects (larger horizons, stronger deflection, bigger shadows, brighter disks) while $Q$ tends to oppose them. The analysis yields concrete observational signatures and parameter constraints, including EHT-based bounds on $\alpha$ for M87* and Sgr A*, and reveals potential degeneracies with Kerr-like spinning spacetimes. The results provide a multi- observational framework to test STVG with upcoming high-precision imaging and lensing campaigns, and suggest extensions to rotating STVG BHs and more realistic plasma environments.

Abstract

We explore charged black holes in Scalar-Tensor-Vector Gravity (STVG), unveiling their distinctive features across multiple physical domains. Our topological analysis reveals that the STVG coupling parameter $α$ bolsters thermal stability while electromagnetic charge $Q$ weakens it. Using the Gauss-Bonnet theorem, we find that $α$ amplifies light deflection and enlarges shadow silhouettes, with $Q$ generating opposite effects. Our quantum-corrected models with exponential entropy terms pinpoint phase transitions in the microscopic regime, modifying conventional thermodynamic relationships. Calculations of strong gravitational lensing, shadow geometry, and Hawking emission show clear STVG signatures that diverge from Einstein's predictions. Notably, our accretion disk analysis uncovers an intriguing phenomenon: specific combinations of $α$ and $Q$ can produce radiation patterns resembling spinning Kerr black holes, creating potential identification challenges for observers. These findings establish concrete observational tests for STVG theory through next generation astronomical imaging and lensing campaigns. By connecting theoretical predictions to measurable quantities, we outline specific pathways to confirm or constrain STVG using data from current and future space telescopes.

Figures (25)

• Figure 1: 3D embedding diagrams of STVG charged BHs for various combinations of $M$, $Q$, and $\alpha$. (a) The Schwarzschild limit ($Q=0$, $\alpha=0$) establishes the uncharged reference geometry with $r_h=2M$. (b–c) Increasing $\alpha$ in the uncharged case enlarges the horizon radius, illustrating the gravitational enhancement predicted by MOG. (d–f) Charged configurations display the interplay between electromagnetic and scalar–tensor–vector effects: larger $\alpha$ mitigates the electromagnetic repulsion and modifies the curvature profile near the event horizon. The red ring denotes the event horizon, while the black spiral trajectory represents an infalling test particle.
• Figure 2: Hawking temperature $T_H$ versus horizon radius $r_h$ for different $\alpha$ values with fixed $M=1$ and $Q=0.5$. Increasing $\alpha$ raises the temperature and shifts its peak to larger $r_h$, reflecting stronger effective gravity and modified thermodynamic behavior.
• Figure 3: Deflection angle $\Theta$ versus impact parameter $b$ for $M=1$ and $Q=0.5$. Increasing $\alpha$ enhances spacetime curvature and light bending, while $\alpha \to 0$ recovers the RN limit of GR.
• Figure 4: Comparison of $\beta(b,\delta)$ density plots for different parameter choices $\alpha$ (0,0.5,1) respectively. The color intensity indicates deflection angle magnitude, showing how increasing $\alpha$ strengthens gravitational lensing across all impact parameters and plasma densities.
• Figure 5: Quantum-corrected internal energy $E_{C}$ versus horizon radius $r_{h}$ for $M=1$ and $Q=0.5$. At small $r_{h}$, negative $E_{C}$ indicates a quantum-unstable phase, while for large $r_{h}$, positive $E_{C}$ reflects classical stability. Higher $\alpha$ values increase $E_{C}$, showing enhanced gravitational self-energy and stability.