Scalar-tensor-vector gravity theory is tested by black hole photon rings

TL;DR

This work tests a modified gravity framework (STVG/MOG) by examining photon rings around a RN black hole within this theory. It derives null geodesics and effective potentials, analyzes photon-sphere and horizon structure as functions of the MOG parameter $\alpha$ and electric charge $Q$, and performs backward ray-tracing to predict observable photon-ring signatures. Using EHT measurements of M87$^*$ and Sgr A$^*$, it derives joint constraints on $\alpha$ and $Q$, finding non-degenerate, model-dependent photon-ring structures that can distinguish quantum-gravity-inspired spacetimes. The results provide a computational basis for testing modified black holes with current and upcoming high-resolution observations, while highlighting the need for more realistic, spinning, and magnetized accretion-flow models in future work.

Abstract

This paper investigates the photon ring and shadow structure of the Reissner-Nordström black hole in the scalar-tensor-vector gravitational framework. The black hole is characterized by the ( MOG) parameter (α) and the charge (Q). The study finds that as (α) increases, the event horizon radius (r_h), photon sphere radius (r_{ph}), and critical impact parameter (b_{ph}) all increase, while these decrease as (Q) increases. The innermost stable circular orbit radius (r_{isco}) exhibits similar monotonic behavior. Ray-tracing shows that as (Q) increases, the impact parameter (b) interval between the lensing ring and photon ring widens; (b_{\text{ph}}) is non-degenerate, and the photon ring radius is uniquely determined by (α) and (Q). Using $EHT$ constraints on (SgrA^*) and (M87^*), the bounds on (α) and (Q) are derived. For (Q = 0), (0.5), and (1), the allowed ranges are (α\in [0, 0.06]), ([0, 0.11]), and ([0.19, 0.36]), respectively. Radiative simulations show that for fixed (Q), larger (α) leads to a larger, non-degenerate photon ring. The Schwarzschild case is approached only when both (α) and (Q) are small. This provides a computational basis for testing modified black holes and offers a non-degenerate observational criterion for distinguishing quantum gravity models, consistent with current $EHT$ data. Future observations with $ngEHT$ and multi-band polarization can further test this. The results suggest that studying the photon ring structure of a Reissner-Nordström black hole in scalar-tensor-vector gravity provides a unique optical diagnostic for potential quantum-gravity tests and black hole properties.

Figures (15)

• Figure 1: Metric function $f(r)$ for various $\alpha$ and $Q$ at $M = 1$, with the Schwarzschild case shown for comparison.
• Figure 2: Variation of $r_{h}$ with the $MOG$ parameter $\alpha$ and the electric charge $Q$.
• Figure 3: Effective potential $V_{\text{eff}} (r)$ for a Schwarzschild black hole and its correspondence to the photon-sphere radius $r_{\text{ph}}$ and the critical impact parameter $b_{\text{ph}}$
• Figure 4: $V_{eff} (r)$ - $r$ curves for $Q=0$ (upper-left), $Q=0.5$ (upper-right), and $Q=1$ (lower-center), shown for $\alpha=0$, $0.25$, and $1$, with the Schwarzschild case added as a benchmark.
• Figure 5: Curve of $n$ versus the impact parameter $b$ for a Schwarzschild black hole, where black denotes Category $1$, orange denotes Category $2$, and red denotes Category $3$.